/* Subroutine */ int zdrvrf3_(integer *nout, integer *nn, integer *nval,
doublereal *thresh, doublecomplex *a, integer *lda, doublecomplex *
arf, doublecomplex *b1, doublecomplex *b2, doublereal *
d_work_zlange__, doublecomplex *z_work_zgeqrf__, doublecomplex *tau)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char uplos[1*2] = "U" "L";
static char forms[1*2] = "N" "C";
static char sides[1*2] = "L" "R";
static char transs[1*2] = "N" "C";
static char diags[1*2] = "N" "U";
/* Format strings */
static char fmt_9999[] = "(1x,\002 *** Error(s) or Failure(s) while test"
"ing ZTFSM ***\002)";
static char fmt_9997[] = "(1x,\002 Failure in \002,a5,\002, CFORM="
"'\002,a1,\002',\002,\002 SIDE='\002,a1,\002',\002,\002 UPLO='"
"\002,a1,\002',\002,\002 TRANS='\002,a1,\002',\002,\002 DIAG='"
"\002,a1,\002',\002,\002 M=\002,i3,\002, N =\002,i3,\002, test"
"=\002,g12.5)";
static char fmt_9996[] = "(1x,\002All tests for \002,a5,\002 auxiliary r"
"outine passed the \002,\002threshold (\002,i5,\002 tests run)"
"\002)";
static char fmt_9995[] = "(1x,a6,\002 auxiliary routine:\002,i5,\002 out"
" of \002,i5,\002 tests failed to pass the threshold\002)";
/* System generated locals */
integer a_dim1, a_offset, b1_dim1, b1_offset, b2_dim1, b2_offset, i__1,
i__2, i__3, i__4, i__5, i__6, i__7;
doublecomplex z__1, z__2;
/* Local variables */
integer i__, j, m, n, na, iim, iin;
doublereal eps;
char diag[1], side[1];
integer info;
char uplo[1];
integer nrun, idiag;
doublecomplex alpha;
integer nfail, iseed[4], iside;
char cform[1];
integer iform;
char trans[1];
integer iuplo;
integer ialpha;
integer itrans;
doublereal result[1];
/* Fortran I/O blocks */
static cilist io___32 = { 0, 0, 0, 0, 0 };
static cilist io___33 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___34 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___35 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___36 = { 0, 0, 0, fmt_9995, 0 };
/* -- LAPACK test routine (version 3.2.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2008 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZDRVRF3 tests the LAPACK RFP routines: */
/* ZTFSM */
/* Arguments */
/* ========= */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix dimension N. */
/* THRESH (input) DOUBLE PRECISION */
/* 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. */
/* A (workspace) COMPLEX*16 array, dimension (LDA,NMAX) */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,NMAX). */
/* ARF (workspace) COMPLEX*16 array, dimension ((NMAX*(NMAX+1))/2). */
/* B1 (workspace) COMPLEX*16 array, dimension (LDA,NMAX) */
/* B2 (workspace) COMPLEX*16 array, dimension (LDA,NMAX) */
/* D_WORK_ZLANGE (workspace) DOUBLE PRECISION array, dimension (NMAX) */
/* Z_WORK_ZGEQRF (workspace) COMPLEX*16 array, dimension (NMAX) */
/* TAU (workspace) COMPLEX*16 array, dimension (NMAX) */
/* ===================================================================== */
/* .. */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--nval;
b2_dim1 = *lda;
b2_offset = 1 + b2_dim1;
b2 -= b2_offset;
b1_dim1 = *lda;
b1_offset = 1 + b1_dim1;
b1 -= b1_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--arf;
--d_work_zlange__;
--z_work_zgeqrf__;
--tau;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
nrun = 0;
nfail = 0;
info = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
eps = dlamch_("Precision");
i__1 = *nn;
for (iim = 1; iim <= i__1; ++iim) {
m = nval[iim];
i__2 = *nn;
for (iin = 1; iin <= i__2; ++iin) {
n = nval[iin];
for (iform = 1; iform <= 2; ++iform) {
*(unsigned char *)cform = *(unsigned char *)&forms[iform - 1];
for (iuplo = 1; iuplo <= 2; ++iuplo) {
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo -
1];
for (iside = 1; iside <= 2; ++iside) {
*(unsigned char *)side = *(unsigned char *)&sides[
iside - 1];
for (itrans = 1; itrans <= 2; ++itrans) {
*(unsigned char *)trans = *(unsigned char *)&
transs[itrans - 1];
for (idiag = 1; idiag <= 2; ++idiag) {
*(unsigned char *)diag = *(unsigned char *)&
diags[idiag - 1];
for (ialpha = 1; ialpha <= 3; ++ialpha) {
if (ialpha == 1) {
alpha.r = 0., alpha.i = 0.;
} else if (ialpha == 1) {
alpha.r = 1., alpha.i = 0.;
} else {
zlarnd_(&z__1, &c__4, iseed);
alpha.r = z__1.r, alpha.i = z__1.i;
}
/* All the parameters are set: */
/* CFORM, SIDE, UPLO, TRANS, DIAG, M, N, */
/* and ALPHA */
/* READY TO TEST! */
++nrun;
if (iside == 1) {
/* The case ISIDE.EQ.1 is when SIDE.EQ.'L' */
/* -> A is M-by-M ( B is M-by-N ) */
na = m;
} else {
/* The case ISIDE.EQ.2 is when SIDE.EQ.'R' */
/* -> A is N-by-N ( B is M-by-N ) */
na = n;
}
/* Generate A our NA--by--NA triangular */
/* matrix. */
/* Our test is based on forward error so we */
/* do want A to be well conditionned! To get */
/* a well-conditionned triangular matrix, we */
/* take the R factor of the QR/LQ factorization */
/* of a random matrix. */
i__3 = na;
for (j = 1; j <= i__3; ++j) {
i__4 = na;
for (i__ = 1; i__ <= i__4; ++i__) {
i__5 = i__ + j * a_dim1;
zlarnd_(&z__1, &c__4, iseed);
a[i__5].r = z__1.r, a[i__5].i =
z__1.i;
}
}
if (iuplo == 1) {
/* The case IUPLO.EQ.1 is when SIDE.EQ.'U' */
/* -> QR factorization. */
s_copy(srnamc_1.srnamt, "ZGEQRF", (
ftnlen)32, (ftnlen)6);
zgeqrf_(&na, &na, &a[a_offset], lda, &
tau[1], &z_work_zgeqrf__[1],
lda, &info);
} else {
/* The case IUPLO.EQ.2 is when SIDE.EQ.'L' */
/* -> QL factorization. */
s_copy(srnamc_1.srnamt, "ZGELQF", (
ftnlen)32, (ftnlen)6);
zgelqf_(&na, &na, &a[a_offset], lda, &
tau[1], &z_work_zgeqrf__[1],
lda, &info);
}
/* After the QR factorization, the diagonal */
/* of A is made of real numbers, we multiply */
/* by a random complex number of absolute */
/* value 1.0E+00. */
i__3 = na;
for (j = 1; j <= i__3; ++j) {
i__4 = j + j * a_dim1;
i__5 = j + j * a_dim1;
zlarnd_(&z__2, &c__5, iseed);
z__1.r = a[i__5].r * z__2.r - a[i__5]
.i * z__2.i, z__1.i = a[i__5]
.r * z__2.i + a[i__5].i *
z__2.r;
a[i__4].r = z__1.r, a[i__4].i =
z__1.i;
}
/* Store a copy of A in RFP format (in ARF). */
s_copy(srnamc_1.srnamt, "ZTRTTF", (ftnlen)
32, (ftnlen)6);
ztrttf_(cform, uplo, &na, &a[a_offset],
lda, &arf[1], &info);
/* Generate B1 our M--by--N right-hand side */
/* and store a copy in B2. */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = m;
for (i__ = 1; i__ <= i__4; ++i__) {
i__5 = i__ + j * b1_dim1;
zlarnd_(&z__1, &c__4, iseed);
b1[i__5].r = z__1.r, b1[i__5].i =
z__1.i;
i__5 = i__ + j * b2_dim1;
i__6 = i__ + j * b1_dim1;
b2[i__5].r = b1[i__6].r, b2[i__5]
.i = b1[i__6].i;
}
}
/* Solve op( A ) X = B or X op( A ) = B */
/* with ZTRSM */
s_copy(srnamc_1.srnamt, "ZTRSM", (ftnlen)
32, (ftnlen)5);
ztrsm_(side, uplo, trans, diag, &m, &n, &
alpha, &a[a_offset], lda, &b1[
b1_offset], lda);
/* Solve op( A ) X = B or X op( A ) = B */
/* with ZTFSM */
s_copy(srnamc_1.srnamt, "ZTFSM", (ftnlen)
32, (ftnlen)5);
ztfsm_(cform, side, uplo, trans, diag, &m,
&n, &alpha, &arf[1], &b2[
b2_offset], lda);
/* Check that the result agrees. */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = m;
for (i__ = 1; i__ <= i__4; ++i__) {
i__5 = i__ + j * b1_dim1;
i__6 = i__ + j * b2_dim1;
i__7 = i__ + j * b1_dim1;
z__1.r = b2[i__6].r - b1[i__7].r,
z__1.i = b2[i__6].i - b1[
i__7].i;
b1[i__5].r = z__1.r, b1[i__5].i =
z__1.i;
}
}
result[0] = zlange_("I", &m, &n, &b1[
b1_offset], lda, &d_work_zlange__[
1]);
/* Computing MAX */
i__3 = max(m,n);
result[0] = result[0] / sqrt(eps) / max(
i__3,1);
if (result[0] >= *thresh) {
if (nfail == 0) {
io___32.ciunit = *nout;
s_wsle(&io___32);
e_wsle();
io___33.ciunit = *nout;
s_wsfe(&io___33);
e_wsfe();
}
io___34.ciunit = *nout;
s_wsfe(&io___34);
do_fio(&c__1, "ZTFSM", (ftnlen)5);
do_fio(&c__1, cform, (ftnlen)1);
do_fio(&c__1, side, (ftnlen)1);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, diag, (ftnlen)1);
do_fio(&c__1, (char *)&m, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[0], (
ftnlen)sizeof(doublereal));
e_wsfe();
++nfail;
}
/* L100: */
}
/* L110: */
}
/* L120: */
}
/* L130: */
}
/* L140: */
}
/* L150: */
}
/* L160: */
}
/* L170: */
}
/* Print a summary of the results. */
if (nfail == 0) {
io___35.ciunit = *nout;
s_wsfe(&io___35);
do_fio(&c__1, "ZTFSM", (ftnlen)5);
do_fio(&c__1, (char *)&nrun, (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___36.ciunit = *nout;
s_wsfe(&io___36);
do_fio(&c__1, "ZTFSM", (ftnlen)5);
do_fio(&c__1, (char *)&nfail, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nrun, (ftnlen)sizeof(integer));
e_wsfe();
}
return 0;
/* End of ZDRVRF3 */
} /* zdrvrf3_ */
/* Double Complex */ VOID zlatm2_(doublecomplex * ret_val, integer *m,
integer *n, integer *i, integer *j, integer *kl, integer *ku, integer
*idist, integer *iseed, doublecomplex *d, integer *igrade,
doublecomplex *dl, doublecomplex *dr, integer *ipvtng, integer *iwork,
doublereal *sparse)
{
/* System generated locals */
integer i__1, i__2;
doublecomplex z__1, z__2, z__3;
/* Builtin functions */
void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg(
doublecomplex *, doublecomplex *);
/* Local variables */
static integer isub, jsub;
static doublecomplex ctemp;
extern doublereal dlaran_(integer *);
extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *,
integer *);
/* -- LAPACK auxiliary test routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
ZLATM2 returns the (I,J) entry of a random matrix of dimension
(M, N) described by the other paramters. It is called by the
ZLATMR routine in order to build random test matrices. No error
checking on parameters is done, because this routine is called in
a tight loop by ZLATMR which has already checked the parameters.
Use of ZLATM2 differs from CLATM3 in the order in which the random
number generator is called to fill in random matrix entries.
With ZLATM2, the generator is called to fill in the pivoted matrix
columnwise. With ZLATM3, the generator is called to fill in the
matrix columnwise, after which it is pivoted. Thus, ZLATM3 can
be used to construct random matrices which differ only in their
order of rows and/or columns. ZLATM2 is used to construct band
matrices while avoiding calling the random number generator for
entries outside the band (and therefore generating random numbers
The matrix whose (I,J) entry is returned is constructed as
follows (this routine only computes one entry):
If I is outside (1..M) or J is outside (1..N), return zero
(this is convenient for generating matrices in band format).
Generate a matrix A with random entries of distribution IDIST.
Set the diagonal to D.
Grade the matrix, if desired, from the left (by DL) and/or
from the right (by DR or DL) as specified by IGRADE.
Permute, if desired, the rows and/or columns as specified by
IPVTNG and IWORK.
Band the matrix to have lower bandwidth KL and upper
bandwidth KU.
Set random entries to zero as specified by SPARSE.
Arguments
=========
M - INTEGER
Number of rows of matrix. Not modified.
N - INTEGER
Number of columns of matrix. Not modified.
I - INTEGER
Row of entry to be returned. Not modified.
J - INTEGER
Column of entry to be returned. Not modified.
KL - INTEGER
Lower bandwidth. Not modified.
KU - INTEGER
Upper bandwidth. Not modified.
IDIST - INTEGER
On entry, IDIST specifies the type of distribution to be
used to generate a random matrix .
1 => real and imaginary parts each UNIFORM( 0, 1 )
2 => real and imaginary parts each UNIFORM( -1, 1 )
3 => real and imaginary parts each NORMAL( 0, 1 )
4 => complex number uniform in DISK( 0 , 1 )
Not modified.
ISEED - INTEGER array of dimension ( 4 )
Seed for random number generator.
Changed on exit.
D - COMPLEX*16 array of dimension ( MIN( I , J ) )
Diagonal entries of matrix. Not modified.
IGRADE - INTEGER
Specifies grading of matrix as follows:
0 => no grading
1 => matrix premultiplied by diag( DL )
2 => matrix postmultiplied by diag( DR )
3 => matrix premultiplied by diag( DL ) and
postmultiplied by diag( DR )
4 => matrix premultiplied by diag( DL ) and
postmultiplied by inv( diag( DL ) )
5 => matrix premultiplied by diag( DL ) and
postmultiplied by diag( CONJG(DL) )
6 => matrix premultiplied by diag( DL ) and
postmultiplied by diag( DL )
Not modified.
DL - COMPLEX*16 array ( I or J, as appropriate )
Left scale factors for grading matrix. Not modified.
DR - COMPLEX*16 array ( I or J, as appropriate )
Right scale factors for grading matrix. Not modified.
IPVTNG - INTEGER
On entry specifies pivoting permutations as follows:
0 => none.
1 => row pivoting.
2 => column pivoting.
3 => full pivoting, i.e., on both sides.
Not modified.
IWORK - INTEGER array ( I or J, as appropriate )
This array specifies the permutation used. The
row (or column) in position K was originally in
position IWORK( K ).
This differs from IWORK for ZLATM3. Not modified.
SPARSE - DOUBLE PRECISION between 0. and 1.
On entry specifies the sparsity of the matrix
if sparse matix is to be generated.
SPARSE should lie between 0 and 1.
A uniform ( 0, 1 ) random number x is generated and
compared to SPARSE; if x is larger the matrix entry
is unchanged and if x is smaller the entry is set
to zero. Thus on the average a fraction SPARSE of the
entries will be set to zero.
Not modified.
=====================================================================
-----------------------------------------------------------------------
Check for I and J in range
Parameter adjustments */
--iwork;
--dr;
--dl;
--d;
--iseed;
/* Function Body */
if (*i < 1 || *i > *m || *j < 1 || *j > *n) {
ret_val->r = 0., ret_val->i = 0.;
return ;
}
/* Check for banding */
if (*j > *i + *ku || *j < *i - *kl) {
ret_val->r = 0., ret_val->i = 0.;
return ;
}
/* Check for sparsity */
if (*sparse > 0.) {
if (dlaran_(&iseed[1]) < *sparse) {
ret_val->r = 0., ret_val->i = 0.;
return ;
}
}
/* Compute subscripts depending on IPVTNG */
if (*ipvtng == 0) {
isub = *i;
jsub = *j;
} else if (*ipvtng == 1) {
isub = iwork[*i];
jsub = *j;
} else if (*ipvtng == 2) {
isub = *i;
jsub = iwork[*j];
} else if (*ipvtng == 3) {
isub = iwork[*i];
jsub = iwork[*j];
}
/* Compute entry and grade it according to IGRADE */
if (isub == jsub) {
i__1 = isub;
ctemp.r = d[i__1].r, ctemp.i = d[i__1].i;
} else {
zlarnd_(&z__1, idist, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
}
if (*igrade == 1) {
i__1 = isub;
z__1.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__1.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 2) {
i__1 = jsub;
z__1.r = ctemp.r * dr[i__1].r - ctemp.i * dr[i__1].i, z__1.i =
ctemp.r * dr[i__1].i + ctemp.i * dr[i__1].r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 3) {
i__1 = isub;
z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
i__2 = jsub;
z__1.r = z__2.r * dr[i__2].r - z__2.i * dr[i__2].i, z__1.i = z__2.r *
dr[i__2].i + z__2.i * dr[i__2].r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 4 && isub != jsub) {
i__1 = isub;
z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
z_div(&z__1, &z__2, &dl[jsub]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 5) {
i__1 = isub;
z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
d_cnjg(&z__3, &dl[jsub]);
z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i
+ z__2.i * z__3.r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 6) {
i__1 = isub;
z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
i__2 = jsub;
z__1.r = z__2.r * dl[i__2].r - z__2.i * dl[i__2].i, z__1.i = z__2.r *
dl[i__2].i + z__2.i * dl[i__2].r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
}
ret_val->r = ctemp.r, ret_val->i = ctemp.i;
return ;
/* End of ZLATM2 */
} /* zlatm2_ */
/* Subroutine */ int zdrges_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, doublereal *thresh, integer *nounit,
doublecomplex *a, integer *lda, doublecomplex *b, doublecomplex *s,
doublecomplex *t, doublecomplex *q, integer *ldq, doublecomplex *z__,
doublecomplex *alpha, doublecomplex *beta, doublecomplex *work,
integer *lwork, doublereal *rwork, doublereal *result, logical *bwork,
integer *info)
{
/* Initialized data */
static integer kclass[26] = { 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,2,3 };
static integer kbmagn[26] = { 1,1,1,1,1,1,1,1,3,2,3,2,2,3,1,1,1,1,1,1,1,3,
2,3,2,1 };
static integer ktrian[26] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,
1,1,1,1 };
static logical lasign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
TRUE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,TRUE_,TRUE_,FALSE_ };
static logical lbsign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_ };
static integer kz1[6] = { 0,1,2,1,3,3 };
static integer kz2[6] = { 0,0,1,2,1,1 };
static integer kadd[6] = { 0,0,0,0,3,2 };
static integer katype[26] = { 0,1,0,1,2,3,4,1,4,4,1,1,4,4,4,2,4,5,8,7,9,4,
4,4,4,0 };
static integer kbtype[26] = { 0,0,1,1,2,-3,1,4,1,1,4,4,1,1,-4,2,-4,8,8,8,
8,8,8,8,8,0 };
static integer kazero[26] = { 1,1,1,1,1,1,2,1,2,2,1,1,2,2,3,1,3,5,5,5,5,3,
3,3,3,1 };
static integer kbzero[26] = { 1,1,1,1,1,1,1,2,1,1,2,2,1,1,4,1,4,6,6,6,6,4,
4,4,4,1 };
static integer kamagn[26] = { 1,1,1,1,1,1,1,1,2,3,2,3,2,3,1,1,1,1,1,1,1,2,
3,3,2,1 };
/* Format strings */
static char fmt_9999[] = "(\002 ZDRGES: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
"(\002,4(i4,\002,\002),i5,\002)\002)";
static char fmt_9998[] = "(\002 ZDRGES: S not in Schur form at eigenvalu"
"e \002,i6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, "
"ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9997[] = "(/1x,a3,\002 -- Complex Generalized Schur from"
" problem \002,\002driver\002)";
static char fmt_9996[] = "(\002 Matrix types (see ZDRGES for details):"
" \002)";
static char fmt_9995[] = "(\002 Special Matrices:\002,23x,\002(J'=transp"
"osed Jordan block)\002,/\002 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I"
") 5=(J',J') \002,\0026=(diag(J',I), diag(I,J'))\002,/\002 Diag"
"onal Matrices: ( \002,\002D=diag(0,1,2,...) )\002,/\002 7=(D,"
"I) 9=(large*D, small*I\002,\002) 11=(large*I, small*D) 13=(l"
"arge*D, large*I)\002,/\002 8=(I,D) 10=(small*D, large*I) 12="
"(small*I, large*D) \002,\002 14=(small*D, small*I)\002,/\002 15"
"=(D, reversed D)\002)";
static char fmt_9994[] = "(\002 Matrices Rotated by Random \002,a,\002 M"
"atrices U, V:\002,/\002 16=Transposed Jordan Blocks "
" 19=geometric \002,\002alpha, beta=0,1\002,/\002 17=arithm. alp"
"ha&beta \002,\002 20=arithmetic alpha, beta=0,"
"1\002,/\002 18=clustered \002,\002alpha, beta=0,1 21"
"=random alpha, beta=0,1\002,/\002 Large & Small Matrices:\002,"
"/\002 22=(large, small) \002,\00223=(small,large) 24=(smal"
"l,small) 25=(large,large)\002,/\002 26=random O(1) matrices"
".\002)";
static char fmt_9993[] = "(/\002 Tests performed: (S is Schur, T is tri"
"angular, \002,\002Q and Z are \002,a,\002,\002,/19x,\002l and r "
"are the appropriate left and right\002,/19x,\002eigenvectors, re"
"sp., a is alpha, b is beta, and\002,/19x,a,\002 means \002,a,"
"\002.)\002,/\002 Without ordering: \002,/\002 1 = | A - Q S "
"Z\002,a,\002 | / ( |A| n ulp ) 2 = | B - Q T Z\002,a,\002 |"
" / ( |B| n ulp )\002,/\002 3 = | I - QQ\002,a,\002 | / ( n ulp "
") 4 = | I - ZZ\002,a,\002 | / ( n ulp )\002,/\002 5"
" = A is in Schur form S\002,/\002 6 = difference between (alpha"
",beta)\002,\002 and diagonals of (S,T)\002,/\002 With ordering:"
" \002,/\002 7 = | (A,B) - Q (S,T) Z\002,a,\002 | / ( |(A,B)| n "
"ulp )\002,/\002 8 = | I - QQ\002,a,\002 | / ( n ulp ) "
" 9 = | I - ZZ\002,a,\002 | / ( n ulp )\002,/\002 10 = A is in "
"Schur form S\002,/\002 11 = difference between (alpha,beta) and "
"diagonals\002,\002 of (S,T)\002,/\002 12 = SDIM is the correct n"
"umber of \002,\002selected eigenvalues\002,/)";
static char fmt_9992[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i2,\002 is\002"
",0p,f8.2)";
static char fmt_9991[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i2,\002 is\002"
",1p,d10.3)";
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, s_dim1,
s_offset, t_dim1, t_offset, z_dim1, z_offset, i__1, i__2, i__3,
i__4, i__5, i__6, i__7, i__8, i__9, i__10, i__11;
doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10,
d__11, d__12, d__13, d__14, d__15, d__16;
doublecomplex z__1, z__2, z__3, z__4;
/* Local variables */
integer i__, j, n, n1, jc, nb, in, jr;
doublereal ulp;
integer iadd, sdim, nmax, rsub;
char sort[1];
doublereal temp1, temp2;
logical badnn;
integer iinfo;
doublereal rmagn[4];
doublecomplex ctemp;
extern /* Subroutine */ int zget51_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *
, doublecomplex *, integer *, doublecomplex *, doublereal *,
doublereal *), zgges_(char *, char *, char *, L_fp, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, logical *, integer *);
integer nmats, jsize;
extern /* Subroutine */ int zget54_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublereal *);
integer nerrs, jtype, ntest, isort;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), zlatm4_(
integer *, integer *, integer *, integer *, logical *, doublereal
*, doublereal *, doublereal *, integer *, integer *,
doublecomplex *, integer *);
logical ilabad;
extern doublereal dlamch_(char *);
extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *);
doublereal safmin, safmax;
integer knteig, ioldsd[4];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer
*, integer *), xerbla_(char *, integer *),
zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *);
extern /* Double Complex */ void zlarnd_(doublecomplex *, integer *,
integer *);
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *);
extern logical zlctes_(doublecomplex *, doublecomplex *);
integer minwrk, maxwrk;
doublereal ulpinv;
integer mtypes, ntestt;
/* Fortran I/O blocks */
static cilist io___41 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___47 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___55 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___56 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___57 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___58 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___59 = { 0, 0, 0, fmt_9991, 0 };
/* -- LAPACK test routine (version 3.1.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* February 2007 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZDRGES checks the nonsymmetric generalized eigenvalue (Schur form) */
/* problem driver ZGGES. */
/* ZGGES factors A and B as Q*S*Z' and Q*T*Z' , where ' means conjugate */
/* transpose, S and T are upper triangular (i.e., in generalized Schur */
/* form), and Q and Z are unitary. It also computes the generalized */
/* eigenvalues (alpha(j),beta(j)), j=1,...,n. Thus, */
/* w(j) = alpha(j)/beta(j) is a root of the characteristic equation */
/* det( A - w(j) B ) = 0 */
/* Optionally it also reorder the eigenvalues so that a selected */
/* cluster of eigenvalues appears in the leading diagonal block of the */
/* Schur forms. */
/* When ZDRGES is called, a number of matrix "sizes" ("N's") and a */
/* number of matrix "TYPES" are specified. For each size ("N") */
/* and each TYPE of matrix, a pair of matrices (A, B) will be generated */
/* and used for testing. For each matrix pair, the following 13 tests */
/* will be performed and compared with the threshhold THRESH except */
/* the tests (5), (11) and (13). */
/* (1) | A - Q S Z' | / ( |A| n ulp ) (no sorting of eigenvalues) */
/* (2) | B - Q T Z' | / ( |B| n ulp ) (no sorting of eigenvalues) */
/* (3) | I - QQ' | / ( n ulp ) (no sorting of eigenvalues) */
/* (4) | I - ZZ' | / ( n ulp ) (no sorting of eigenvalues) */
/* (5) if A is in Schur form (i.e. triangular form) (no sorting of */
/* eigenvalues) */
/* (6) if eigenvalues = diagonal elements of the Schur form (S, T), */
/* i.e., test the maximum over j of D(j) where: */
/* |alpha(j) - S(j,j)| |beta(j) - T(j,j)| */
/* D(j) = ------------------------ + ----------------------- */
/* max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) */
/* (no sorting of eigenvalues) */
/* (7) | (A,B) - Q (S,T) Z' | / ( |(A,B)| n ulp ) */
/* (with sorting of eigenvalues). */
/* (8) | I - QQ' | / ( n ulp ) (with sorting of eigenvalues). */
/* (9) | I - ZZ' | / ( n ulp ) (with sorting of eigenvalues). */
/* (10) if A is in Schur form (i.e. quasi-triangular form) */
/* (with sorting of eigenvalues). */
/* (11) if eigenvalues = diagonal elements of the Schur form (S, T), */
/* i.e. test the maximum over j of D(j) where: */
/* |alpha(j) - S(j,j)| |beta(j) - T(j,j)| */
/* D(j) = ------------------------ + ----------------------- */
/* max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) */
/* (with sorting of eigenvalues). */
/* (12) if sorting worked and SDIM is the number of eigenvalues */
/* which were CELECTed. */
/* Test Matrices */
/* ============= */
/* The sizes of the test matrices are specified by an array */
/* NN(1:NSIZES); the value of each element NN(j) specifies one size. */
/* The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if */
/* DOTYPE(j) is .TRUE., then matrix type "j" will be generated. */
/* Currently, the list of possible types is: */
/* (1) ( 0, 0 ) (a pair of zero matrices) */
/* (2) ( I, 0 ) (an identity and a zero matrix) */
/* (3) ( 0, I ) (an identity and a zero matrix) */
/* (4) ( I, I ) (a pair of identity matrices) */
/* t t */
/* (5) ( J , J ) (a pair of transposed Jordan blocks) */
/* t ( I 0 ) */
/* (6) ( X, Y ) where X = ( J 0 ) and Y = ( t ) */
/* ( 0 I ) ( 0 J ) */
/* and I is a k x k identity and J a (k+1)x(k+1) */
/* Jordan block; k=(N-1)/2 */
/* (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal */
/* matrix with those diagonal entries.) */
/* (8) ( I, D ) */
/* (9) ( big*D, small*I ) where "big" is near overflow and small=1/big */
/* (10) ( small*D, big*I ) */
/* (11) ( big*I, small*D ) */
/* (12) ( small*I, big*D ) */
/* (13) ( big*D, big*I ) */
/* (14) ( small*D, small*I ) */
/* (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and */
/* D2 is diag( 0, N-3, N-4,..., 1, 0, 0 ) */
/* t t */
/* (16) Q ( J , J ) Z where Q and Z are random orthogonal matrices. */
/* (17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices */
/* with random O(1) entries above the diagonal */
/* and diagonal entries diag(T1) = */
/* ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = */
/* ( 0, N-3, N-4,..., 1, 0, 0 ) */
/* (18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) */
/* s = machine precision. */
/* (19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 ) */
/* N-5 */
/* (20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) */
/* (21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) */
/* where r1,..., r(N-4) are random. */
/* (22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular */
/* matrices. */
/* Arguments */
/* ========= */
/* NSIZES (input) INTEGER */
/* The number of sizes of matrices to use. If it is zero, */
/* DDRGES does nothing. NSIZES >= 0. */
/* NN (input) INTEGER array, dimension (NSIZES) */
/* An array containing the sizes to be used for the matrices. */
/* Zero values will be skipped. NN >= 0. */
/* NTYPES (input) INTEGER */
/* The number of elements in DOTYPE. If it is zero, DDRGES */
/* 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 on input. */
/* This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and */
/* DOTYPE(MAXTYP+1) is .TRUE. . */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* If DOTYPE(j) is .TRUE., then for each size in NN a */
/* matrix of that size and of type j will be generated. */
/* If NTYPES is smaller than the maximum number of types */
/* defined (PARAMETER MAXTYP), then types NTYPES+1 through */
/* MAXTYP will not be generated. If NTYPES is larger */
/* than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) */
/* will be ignored. */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry ISEED specifies the seed of the random number */
/* generator. The array elements should be between 0 and 4095; */
/* if not they will be reduced mod 4096. Also, ISEED(4) must */
/* be odd. The random number generator uses a linear */
/* congruential sequence limited to small integers, and so */
/* should produce machine independent random numbers. The */
/* values of ISEED are changed on exit, and can be used in the */
/* next call to DDRGES to continue the same random number */
/* sequence. */
/* THRESH (input) DOUBLE PRECISION */
/* A test will count as "failed" if the "error", computed as */
/* described above, exceeds THRESH. Note that the error is */
/* scaled to be O(1), so THRESH should be a reasonably small */
/* multiple of 1, e.g., 10 or 100. In particular, it should */
/* not depend on the precision (single vs. double) or the size */
/* of the matrix. THRESH >= 0. */
/* NOUNIT (input) INTEGER */
/* The FORTRAN unit number for printing out error messages */
/* (e.g., if a routine returns IINFO not equal to 0.) */
/* A (input/workspace) COMPLEX*16 array, dimension(LDA, max(NN)) */
/* Used to hold the original A matrix. Used as input only */
/* if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and */
/* DOTYPE(MAXTYP+1)=.TRUE. */
/* LDA (input) INTEGER */
/* The leading dimension of A, B, S, and T. */
/* It must be at least 1 and at least max( NN ). */
/* B (input/workspace) COMPLEX*16 array, dimension(LDA, max(NN)) */
/* Used to hold the original B matrix. Used as input only */
/* if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and */
/* DOTYPE(MAXTYP+1)=.TRUE. */
/* S (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* The Schur form matrix computed from A by ZGGES. On exit, S */
/* contains the Schur form matrix corresponding to the matrix */
/* in A. */
/* T (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* The upper triangular matrix computed from B by ZGGES. */
/* Q (workspace) COMPLEX*16 array, dimension (LDQ, max(NN)) */
/* The (left) orthogonal matrix computed by ZGGES. */
/* LDQ (input) INTEGER */
/* The leading dimension of Q and Z. It must */
/* be at least 1 and at least max( NN ). */
/* Z (workspace) COMPLEX*16 array, dimension( LDQ, max(NN) ) */
/* The (right) orthogonal matrix computed by ZGGES. */
/* ALPHA (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* BETA (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* The generalized eigenvalues of (A,B) computed by ZGGES. */
/* ALPHA(k) / BETA(k) is the k-th generalized eigenvalue of A */
/* and B. */
/* WORK (workspace) COMPLEX*16 array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= 3*N*N. */
/* RWORK (workspace) DOUBLE PRECISION array, dimension ( 8*N ) */
/* Real workspace. */
/* RESULT (output) DOUBLE PRECISION array, dimension (15) */
/* The values computed by the tests described above. */
/* The values are currently limited to 1/ulp, to avoid overflow. */
/* BWORK (workspace) LOGICAL array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: A routine returned an error code. INFO is the */
/* absolute value of the INFO value returned. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--nn;
--dotype;
--iseed;
t_dim1 = *lda;
t_offset = 1 + t_dim1;
t -= t_offset;
s_dim1 = *lda;
s_offset = 1 + s_dim1;
s -= s_offset;
b_dim1 = *lda;
b_offset = 1 + b_dim1;
b -= b_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
z_dim1 = *ldq;
z_offset = 1 + z_dim1;
z__ -= z_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--alpha;
--beta;
--work;
--rwork;
--result;
--bwork;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
*info = 0;
badnn = FALSE_;
nmax = 1;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = nmax, i__3 = nn[j];
nmax = max(i__2,i__3);
if (nn[j] < 0) {
badnn = TRUE_;
}
/* L10: */
}
if (*nsizes < 0) {
*info = -1;
} else if (badnn) {
*info = -2;
} else if (*ntypes < 0) {
*info = -3;
} else if (*thresh < 0.) {
*info = -6;
} else if (*lda <= 1 || *lda < nmax) {
*info = -9;
} else if (*ldq <= 1 || *ldq < nmax) {
*info = -14;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. */
minwrk = 1;
if (*info == 0 && *lwork >= 1) {
minwrk = nmax * 3 * nmax;
/* Computing MAX */
i__1 = 1, i__2 = ilaenv_(&c__1, "ZGEQRF", " ", &nmax, &nmax, &c_n1, &
c_n1), i__1 = max(i__1,i__2), i__2 =
ilaenv_(&c__1, "ZUNMQR", "LC", &nmax, &nmax, &nmax, &c_n1), i__1 = max(i__1,i__2), i__2 = ilaenv_(&
c__1, "ZUNGQR", " ", &nmax, &nmax, &nmax, &c_n1);
nb = max(i__1,i__2);
/* Computing MAX */
i__1 = nmax + nmax * nb, i__2 = nmax * 3 * nmax;
maxwrk = max(i__1,i__2);
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
}
if (*lwork < minwrk) {
*info = -19;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZDRGES", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
ulp = dlamch_("Precision");
safmin = dlamch_("Safe minimum");
safmin /= ulp;
safmax = 1. / safmin;
dlabad_(&safmin, &safmax);
ulpinv = 1. / ulp;
/* The values RMAGN(2:3) depend on N, see below. */
rmagn[0] = 0.;
rmagn[1] = 1.;
/* Loop over matrix sizes */
ntestt = 0;
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
n1 = max(1,n);
rmagn[2] = safmax * ulp / (doublereal) n1;
rmagn[3] = safmin * ulpinv * (doublereal) n1;
if (*nsizes != 1) {
mtypes = min(26,*ntypes);
} else {
mtypes = min(27,*ntypes);
}
/* Loop over matrix types */
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L180;
}
++nmats;
ntest = 0;
/* Save ISEED in case of an error. */
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
/* Initialize RESULT */
for (j = 1; j <= 13; ++j) {
result[j] = 0.;
/* L30: */
}
/* Generate test matrices A and B */
/* Description of control parameters: */
/* KZLASS: =1 means w/o rotation, =2 means w/ rotation, */
/* =3 means random. */
/* KATYPE: the "type" to be passed to ZLATM4 for computing A. */
/* KAZERO: the pattern of zeros on the diagonal for A: */
/* =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ), */
/* =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ), */
/* =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of */
/* non-zero entries.) */
/* KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1), */
/* =2: large, =3: small. */
/* LASIGN: .TRUE. if the diagonal elements of A are to be */
/* multiplied by a random magnitude 1 number. */
/* KBTYPE, KBZERO, KBMAGN, LBSIGN: the same, but for B. */
/* KTRIAN: =0: don't fill in the upper triangle, =1: do. */
/* KZ1, KZ2, KADD: used to implement KAZERO and KBZERO. */
/* RMAGN: used to implement KAMAGN and KBMAGN. */
if (mtypes > 26) {
goto L110;
}
iinfo = 0;
if (kclass[jtype - 1] < 3) {
/* Generate A (w/o rotation) */
if ((i__3 = katype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
zlaset_("Full", &n, &n, &c_b1, &c_b1, &a[a_offset],
lda);
}
} else {
in = n;
}
zlatm4_(&katype[jtype - 1], &in, &kz1[kazero[jtype - 1] - 1],
&kz2[kazero[jtype - 1] - 1], &lasign[jtype - 1], &
rmagn[kamagn[jtype - 1]], &ulp, &rmagn[ktrian[jtype -
1] * kamagn[jtype - 1]], &c__2, &iseed[1], &a[
a_offset], lda);
iadd = kadd[kazero[jtype - 1] - 1];
if (iadd > 0 && iadd <= n) {
i__3 = iadd + iadd * a_dim1;
i__4 = kamagn[jtype - 1];
a[i__3].r = rmagn[i__4], a[i__3].i = 0.;
}
/* Generate B (w/o rotation) */
if ((i__3 = kbtype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
zlaset_("Full", &n, &n, &c_b1, &c_b1, &b[b_offset],
lda);
}
} else {
in = n;
}
zlatm4_(&kbtype[jtype - 1], &in, &kz1[kbzero[jtype - 1] - 1],
&kz2[kbzero[jtype - 1] - 1], &lbsign[jtype - 1], &
rmagn[kbmagn[jtype - 1]], &c_b29, &rmagn[ktrian[jtype
- 1] * kbmagn[jtype - 1]], &c__2, &iseed[1], &b[
b_offset], lda);
iadd = kadd[kbzero[jtype - 1] - 1];
if (iadd != 0 && iadd <= n) {
i__3 = iadd + iadd * b_dim1;
i__4 = kbmagn[jtype - 1];
b[i__3].r = rmagn[i__4], b[i__3].i = 0.;
}
if (kclass[jtype - 1] == 2 && n > 0) {
/* Include rotations */
/* Generate Q, Z as Householder transformations times */
/* a diagonal matrix. */
i__3 = n - 1;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = jc; jr <= i__4; ++jr) {
i__5 = jr + jc * q_dim1;
zlarnd_(&z__1, &c__3, &iseed[1]);
q[i__5].r = z__1.r, q[i__5].i = z__1.i;
i__5 = jr + jc * z_dim1;
zlarnd_(&z__1, &c__3, &iseed[1]);
z__[i__5].r = z__1.r, z__[i__5].i = z__1.i;
/* L40: */
}
i__4 = n + 1 - jc;
zlarfg_(&i__4, &q[jc + jc * q_dim1], &q[jc + 1 + jc *
q_dim1], &c__1, &work[jc]);
i__4 = (n << 1) + jc;
i__5 = jc + jc * q_dim1;
d__2 = q[i__5].r;
d__1 = d_sign(&c_b29, &d__2);
work[i__4].r = d__1, work[i__4].i = 0.;
i__4 = jc + jc * q_dim1;
q[i__4].r = 1., q[i__4].i = 0.;
i__4 = n + 1 - jc;
zlarfg_(&i__4, &z__[jc + jc * z_dim1], &z__[jc + 1 +
jc * z_dim1], &c__1, &work[n + jc]);
i__4 = n * 3 + jc;
i__5 = jc + jc * z_dim1;
d__2 = z__[i__5].r;
d__1 = d_sign(&c_b29, &d__2);
work[i__4].r = d__1, work[i__4].i = 0.;
i__4 = jc + jc * z_dim1;
z__[i__4].r = 1., z__[i__4].i = 0.;
/* L50: */
}
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__3 = n + n * q_dim1;
q[i__3].r = 1., q[i__3].i = 0.;
i__3 = n;
work[i__3].r = 0., work[i__3].i = 0.;
i__3 = n * 3;
d__1 = z_abs(&ctemp);
z__1.r = ctemp.r / d__1, z__1.i = ctemp.i / d__1;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__3 = n + n * z_dim1;
z__[i__3].r = 1., z__[i__3].i = 0.;
i__3 = n << 1;
work[i__3].r = 0., work[i__3].i = 0.;
i__3 = n << 2;
d__1 = z_abs(&ctemp);
z__1.r = ctemp.r / d__1, z__1.i = ctemp.i / d__1;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
/* Apply the diagonal matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = jr + jc * a_dim1;
i__6 = (n << 1) + jr;
d_cnjg(&z__3, &work[n * 3 + jc]);
z__2.r = work[i__6].r * z__3.r - work[i__6].i *
z__3.i, z__2.i = work[i__6].r * z__3.i +
work[i__6].i * z__3.r;
i__7 = jr + jc * a_dim1;
z__1.r = z__2.r * a[i__7].r - z__2.i * a[i__7].i,
z__1.i = z__2.r * a[i__7].i + z__2.i * a[
i__7].r;
a[i__5].r = z__1.r, a[i__5].i = z__1.i;
i__5 = jr + jc * b_dim1;
i__6 = (n << 1) + jr;
d_cnjg(&z__3, &work[n * 3 + jc]);
z__2.r = work[i__6].r * z__3.r - work[i__6].i *
z__3.i, z__2.i = work[i__6].r * z__3.i +
work[i__6].i * z__3.r;
i__7 = jr + jc * b_dim1;
z__1.r = z__2.r * b[i__7].r - z__2.i * b[i__7].i,
z__1.i = z__2.r * b[i__7].i + z__2.i * b[
i__7].r;
b[i__5].r = z__1.r, b[i__5].i = z__1.i;
/* L60: */
}
/* L70: */
}
i__3 = n - 1;
zunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &a[a_offset], lda, &work[(n << 1) + 1], &
iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
zunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &a[a_offset], lda, &work[(n << 1) +
1], &iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
zunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &b[b_offset], lda, &work[(n << 1) + 1], &
iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
zunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &b[b_offset], lda, &work[(n << 1) +
1], &iinfo);
if (iinfo != 0) {
goto L100;
}
}
} else {
/* Random matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = jr + jc * a_dim1;
i__6 = kamagn[jtype - 1];
zlarnd_(&z__2, &c__4, &iseed[1]);
z__1.r = rmagn[i__6] * z__2.r, z__1.i = rmagn[i__6] *
z__2.i;
a[i__5].r = z__1.r, a[i__5].i = z__1.i;
i__5 = jr + jc * b_dim1;
i__6 = kbmagn[jtype - 1];
zlarnd_(&z__2, &c__4, &iseed[1]);
z__1.r = rmagn[i__6] * z__2.r, z__1.i = rmagn[i__6] *
z__2.i;
b[i__5].r = z__1.r, b[i__5].i = z__1.i;
/* L80: */
}
/* L90: */
}
}
L100:
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;
}
L110:
for (i__ = 1; i__ <= 13; ++i__) {
result[i__] = -1.;
/* L120: */
}
/* Test with and without sorting of eigenvalues */
for (isort = 0; isort <= 1; ++isort) {
if (isort == 0) {
*(unsigned char *)sort = 'N';
rsub = 0;
} else {
*(unsigned char *)sort = 'S';
rsub = 5;
}
/* Call ZGGES to compute H, T, Q, Z, alpha, and beta. */
zlacpy_("Full", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
zlacpy_("Full", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
ntest = rsub + 1 + isort;
result[rsub + 1 + isort] = ulpinv;
zgges_("V", "V", sort, (L_fp)zlctes_, &n, &s[s_offset], lda, &
t[t_offset], lda, &sdim, &alpha[1], &beta[1], &q[
q_offset], ldq, &z__[z_offset], ldq, &work[1], lwork,
&rwork[1], &bwork[1], &iinfo);
if (iinfo != 0 && iinfo != n + 2) {
result[rsub + 1 + isort] = ulpinv;
io___47.ciunit = *nounit;
s_wsfe(&io___47);
do_fio(&c__1, "ZGGES", (ftnlen)5);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
*info = abs(iinfo);
goto L160;
}
ntest = rsub + 4;
/* Do tests 1--4 (or tests 7--9 when reordering ) */
if (isort == 0) {
zget51_(&c__1, &n, &a[a_offset], lda, &s[s_offset], lda, &
q[q_offset], ldq, &z__[z_offset], ldq, &work[1], &
rwork[1], &result[1]);
zget51_(&c__1, &n, &b[b_offset], lda, &t[t_offset], lda, &
q[q_offset], ldq, &z__[z_offset], ldq, &work[1], &
rwork[1], &result[2]);
} else {
zget54_(&n, &a[a_offset], lda, &b[b_offset], lda, &s[
s_offset], lda, &t[t_offset], lda, &q[q_offset],
ldq, &z__[z_offset], ldq, &work[1], &result[rsub
+ 2]);
}
zget51_(&c__3, &n, &b[b_offset], lda, &t[t_offset], lda, &q[
q_offset], ldq, &q[q_offset], ldq, &work[1], &rwork[1]
, &result[rsub + 3]);
zget51_(&c__3, &n, &b[b_offset], lda, &t[t_offset], lda, &z__[
z_offset], ldq, &z__[z_offset], ldq, &work[1], &rwork[
1], &result[rsub + 4]);
/* Do test 5 and 6 (or Tests 10 and 11 when reordering): */
/* check Schur form of A and compare eigenvalues with */
/* diagonals. */
ntest = rsub + 6;
temp1 = 0.;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
ilabad = FALSE_;
i__4 = j;
i__5 = j + j * s_dim1;
z__2.r = alpha[i__4].r - s[i__5].r, z__2.i = alpha[i__4]
.i - s[i__5].i;
z__1.r = z__2.r, z__1.i = z__2.i;
i__6 = j;
i__7 = j + j * t_dim1;
z__4.r = beta[i__6].r - t[i__7].r, z__4.i = beta[i__6].i
- t[i__7].i;
z__3.r = z__4.r, z__3.i = z__4.i;
/* Computing MAX */
i__8 = j;
i__9 = j + j * s_dim1;
d__13 = safmin, d__14 = (d__1 = alpha[i__8].r, abs(d__1))
+ (d__2 = d_imag(&alpha[j]), abs(d__2)), d__13 =
max(d__13,d__14), d__14 = (d__3 = s[i__9].r, abs(
d__3)) + (d__4 = d_imag(&s[j + j * s_dim1]), abs(
d__4));
/* Computing MAX */
i__10 = j;
i__11 = j + j * t_dim1;
d__15 = safmin, d__16 = (d__5 = beta[i__10].r, abs(d__5))
+ (d__6 = d_imag(&beta[j]), abs(d__6)), d__15 =
max(d__15,d__16), d__16 = (d__7 = t[i__11].r, abs(
d__7)) + (d__8 = d_imag(&t[j + j * t_dim1]), abs(
d__8));
temp2 = (((d__9 = z__1.r, abs(d__9)) + (d__10 = d_imag(&
z__1), abs(d__10))) / max(d__13,d__14) + ((d__11 =
z__3.r, abs(d__11)) + (d__12 = d_imag(&z__3),
abs(d__12))) / max(d__15,d__16)) / ulp;
if (j < n) {
i__4 = j + 1 + j * s_dim1;
if (s[i__4].r != 0. || s[i__4].i != 0.) {
ilabad = TRUE_;
result[rsub + 5] = ulpinv;
}
}
if (j > 1) {
i__4 = j + (j - 1) * s_dim1;
if (s[i__4].r != 0. || s[i__4].i != 0.) {
ilabad = TRUE_;
result[rsub + 5] = ulpinv;
}
}
temp1 = max(temp1,temp2);
if (ilabad) {
io___51.ciunit = *nounit;
s_wsfe(&io___51);
do_fio(&c__1, (char *)&j, (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();
}
/* L130: */
}
result[rsub + 6] = temp1;
if (isort >= 1) {
/* Do test 12 */
ntest = 12;
result[12] = 0.;
knteig = 0;
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
if (zlctes_(&alpha[i__], &beta[i__])) {
++knteig;
}
/* L140: */
}
if (sdim != knteig) {
result[13] = ulpinv;
}
}
/* L150: */
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L160:
ntestt += ntest;
/* Print out tests which fail. */
i__3 = ntest;
for (jr = 1; jr <= i__3; ++jr) {
if (result[jr] >= *thresh) {
/* If this is the first test to fail, */
/* print a header to the data file. */
if (nerrs == 0) {
io___53.ciunit = *nounit;
s_wsfe(&io___53);
do_fio(&c__1, "ZGS", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___54.ciunit = *nounit;
s_wsfe(&io___54);
e_wsfe();
io___55.ciunit = *nounit;
s_wsfe(&io___55);
e_wsfe();
io___56.ciunit = *nounit;
s_wsfe(&io___56);
do_fio(&c__1, "Unitary", (ftnlen)7);
e_wsfe();
/* Tests performed */
io___57.ciunit = *nounit;
s_wsfe(&io___57);
do_fio(&c__1, "unitary", (ftnlen)7);
do_fio(&c__1, "'", (ftnlen)1);
do_fio(&c__1, "transpose", (ftnlen)9);
for (j = 1; j <= 8; ++j) {
do_fio(&c__1, "'", (ftnlen)1);
}
e_wsfe();
}
++nerrs;
if (result[jr] < 1e4) {
io___58.ciunit = *nounit;
s_wsfe(&io___58);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
} else {
io___59.ciunit = *nounit;
s_wsfe(&io___59);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
}
}
/* L170: */
}
L180:
;
}
/* L190: */
}
/* Summary */
alasvm_("ZGS", nounit, &nerrs, &ntestt, &c__0);
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
return 0;
/* End of ZDRGES */
} /* zdrges_ */
/* Subroutine */ int zlatm4_(integer *itype, integer *n, integer *nz1,
integer *nz2, logical *rsign, doublereal *amagn, doublereal *rcond,
doublereal *triang, integer *idist, integer *iseed, doublecomplex *a,
integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
doublecomplex z__1, z__2;
/* Local variables */
integer i__, k, jc, jd, jr, kbeg, isdb, kend, isde, klen;
doublereal alpha;
doublecomplex ctemp;
extern doublereal dlaran_(integer *);
extern /* Double Complex */ void zlarnd_(doublecomplex *, integer *,
integer *);
extern /* Subroutine */ int zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *);
/* -- LAPACK auxiliary test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLATM4 generates basic square matrices, which may later be */
/* multiplied by others in order to produce test matrices. It is */
/* intended mainly to be used to test the generalized eigenvalue */
/* routines. */
/* It first generates the diagonal and (possibly) subdiagonal, */
/* according to the value of ITYPE, NZ1, NZ2, RSIGN, AMAGN, and RCOND. */
/* It then fills in the upper triangle with random numbers, if TRIANG is */
/* non-zero. */
/* Arguments */
/* ========= */
/* ITYPE (input) INTEGER */
/* The "type" of matrix on the diagonal and sub-diagonal. */
/* If ITYPE < 0, then type abs(ITYPE) is generated and then */
/* swapped end for end (A(I,J) := A'(N-J,N-I).) See also */
/* the description of AMAGN and RSIGN. */
/* Special types: */
/* = 0: the zero matrix. */
/* = 1: the identity. */
/* = 2: a transposed Jordan block. */
/* = 3: If N is odd, then a k+1 x k+1 transposed Jordan block */
/* followed by a k x k identity block, where k=(N-1)/2. */
/* If N is even, then k=(N-2)/2, and a zero diagonal entry */
/* is tacked onto the end. */
/* Diagonal types. The diagonal consists of NZ1 zeros, then */
/* k=N-NZ1-NZ2 nonzeros. The subdiagonal is zero. ITYPE */
/* specifies the nonzero diagonal entries as follows: */
/* = 4: 1, ..., k */
/* = 5: 1, RCOND, ..., RCOND */
/* = 6: 1, ..., 1, RCOND */
/* = 7: 1, a, a^2, ..., a^(k-1)=RCOND */
/* = 8: 1, 1-d, 1-2*d, ..., 1-(k-1)*d=RCOND */
/* = 9: random numbers chosen from (RCOND,1) */
/* = 10: random numbers with distribution IDIST (see ZLARND.) */
/* N (input) INTEGER */
/* The order of the matrix. */
/* NZ1 (input) INTEGER */
/* If abs(ITYPE) > 3, then the first NZ1 diagonal entries will */
/* be zero. */
/* NZ2 (input) INTEGER */
/* If abs(ITYPE) > 3, then the last NZ2 diagonal entries will */
/* be zero. */
/* RSIGN (input) LOGICAL */
/* = .TRUE.: The diagonal and subdiagonal entries will be */
/* multiplied by random numbers of magnitude 1. */
/* = .FALSE.: The diagonal and subdiagonal entries will be */
/* left as they are (usually non-negative real.) */
/* AMAGN (input) DOUBLE PRECISION */
/* The diagonal and subdiagonal entries will be multiplied by */
/* AMAGN. */
/* RCOND (input) DOUBLE PRECISION */
/* If abs(ITYPE) > 4, then the smallest diagonal entry will be */
/* RCOND. RCOND must be between 0 and 1. */
/* TRIANG (input) DOUBLE PRECISION */
/* The entries above the diagonal will be random numbers with */
/* magnitude bounded by TRIANG (i.e., random numbers multiplied */
/* by TRIANG.) */
/* IDIST (input) INTEGER */
/* On entry, DIST specifies the type of distribution to be used */
/* to generate a random matrix . */
/* = 1: real and imaginary parts each UNIFORM( 0, 1 ) */
/* = 2: real and imaginary parts each UNIFORM( -1, 1 ) */
/* = 3: real and imaginary parts each NORMAL( 0, 1 ) */
/* = 4: complex number uniform in DISK( 0, 1 ) */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry ISEED specifies the seed of the random number */
/* generator. The values of ISEED are changed on exit, and can */
/* be used in the next call to ZLATM4 to continue the same */
/* random number sequence. */
/* Note: ISEED(4) should be odd, for the random number generator */
/* used at present. */
/* A (output) COMPLEX*16 array, dimension (LDA, N) */
/* Array to be computed. */
/* LDA (input) INTEGER */
/* Leading dimension of A. Must be at least 1 and at least N. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--iseed;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
if (*n <= 0) {
return 0;
}
zlaset_("Full", n, n, &c_b1, &c_b1, &a[a_offset], lda);
/* Insure a correct ISEED */
if (iseed[4] % 2 != 1) {
++iseed[4];
}
/* Compute diagonal and subdiagonal according to ITYPE, NZ1, NZ2, */
/* and RCOND */
if (*itype != 0) {
if (abs(*itype) >= 4) {
/* Computing MAX */
/* Computing MIN */
i__3 = *n, i__4 = *nz1 + 1;
i__1 = 1, i__2 = min(i__3,i__4);
kbeg = max(i__1,i__2);
/* Computing MAX */
/* Computing MIN */
i__3 = *n, i__4 = *n - *nz2;
i__1 = kbeg, i__2 = min(i__3,i__4);
kend = max(i__1,i__2);
klen = kend + 1 - kbeg;
} else {
kbeg = 1;
kend = *n;
klen = *n;
}
isdb = 1;
isde = 0;
switch (abs(*itype)) {
case 1: goto L10;
case 2: goto L30;
case 3: goto L50;
case 4: goto L80;
case 5: goto L100;
case 6: goto L120;
case 7: goto L140;
case 8: goto L160;
case 9: goto L180;
case 10: goto L200;
}
/* abs(ITYPE) = 1: Identity */
L10:
i__1 = *n;
for (jd = 1; jd <= i__1; ++jd) {
i__2 = jd + jd * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* L20: */
}
goto L220;
/* abs(ITYPE) = 2: Transposed Jordan block */
L30:
i__1 = *n - 1;
for (jd = 1; jd <= i__1; ++jd) {
i__2 = jd + 1 + jd * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* L40: */
}
isdb = 1;
isde = *n - 1;
goto L220;
/* abs(ITYPE) = 3: Transposed Jordan block, followed by the */
/* identity. */
L50:
k = (*n - 1) / 2;
i__1 = k;
for (jd = 1; jd <= i__1; ++jd) {
i__2 = jd + 1 + jd * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* L60: */
}
isdb = 1;
isde = k;
i__1 = (k << 1) + 1;
for (jd = k + 2; jd <= i__1; ++jd) {
i__2 = jd + jd * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* L70: */
}
goto L220;
/* abs(ITYPE) = 4: 1,...,k */
L80:
i__1 = kend;
for (jd = kbeg; jd <= i__1; ++jd) {
i__2 = jd + jd * a_dim1;
i__3 = jd - *nz1;
z__1.r = (doublereal) i__3, z__1.i = 0.;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L90: */
}
goto L220;
/* abs(ITYPE) = 5: One large D value: */
L100:
i__1 = kend;
for (jd = kbeg + 1; jd <= i__1; ++jd) {
i__2 = jd + jd * a_dim1;
z__1.r = *rcond, z__1.i = 0.;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L110: */
}
i__1 = kbeg + kbeg * a_dim1;
a[i__1].r = 1., a[i__1].i = 0.;
goto L220;
/* abs(ITYPE) = 6: One small D value: */
L120:
i__1 = kend - 1;
for (jd = kbeg; jd <= i__1; ++jd) {
i__2 = jd + jd * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* L130: */
}
i__1 = kend + kend * a_dim1;
z__1.r = *rcond, z__1.i = 0.;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
goto L220;
/* abs(ITYPE) = 7: Exponentially distributed D values: */
L140:
i__1 = kbeg + kbeg * a_dim1;
a[i__1].r = 1., a[i__1].i = 0.;
if (klen > 1) {
d__1 = 1. / (doublereal) (klen - 1);
alpha = pow_dd(rcond, &d__1);
i__1 = klen;
for (i__ = 2; i__ <= i__1; ++i__) {
i__2 = *nz1 + i__ + (*nz1 + i__) * a_dim1;
d__2 = (doublereal) (i__ - 1);
d__1 = pow_dd(&alpha, &d__2);
z__1.r = d__1, z__1.i = 0.;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L150: */
}
}
goto L220;
/* abs(ITYPE) = 8: Arithmetically distributed D values: */
L160:
i__1 = kbeg + kbeg * a_dim1;
a[i__1].r = 1., a[i__1].i = 0.;
if (klen > 1) {
alpha = (1. - *rcond) / (doublereal) (klen - 1);
i__1 = klen;
for (i__ = 2; i__ <= i__1; ++i__) {
i__2 = *nz1 + i__ + (*nz1 + i__) * a_dim1;
d__1 = (doublereal) (klen - i__) * alpha + *rcond;
z__1.r = d__1, z__1.i = 0.;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L170: */
}
}
goto L220;
/* abs(ITYPE) = 9: Randomly distributed D values on ( RCOND, 1): */
L180:
alpha = log(*rcond);
i__1 = kend;
for (jd = kbeg; jd <= i__1; ++jd) {
i__2 = jd + jd * a_dim1;
d__1 = exp(alpha * dlaran_(&iseed[1]));
a[i__2].r = d__1, a[i__2].i = 0.;
/* L190: */
}
goto L220;
/* abs(ITYPE) = 10: Randomly distributed D values from DIST */
L200:
i__1 = kend;
for (jd = kbeg; jd <= i__1; ++jd) {
i__2 = jd + jd * a_dim1;
zlarnd_(&z__1, idist, &iseed[1]);
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L210: */
}
L220:
/* Scale by AMAGN */
i__1 = kend;
for (jd = kbeg; jd <= i__1; ++jd) {
i__2 = jd + jd * a_dim1;
i__3 = jd + jd * a_dim1;
d__1 = *amagn * a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
/* L230: */
}
i__1 = isde;
for (jd = isdb; jd <= i__1; ++jd) {
i__2 = jd + 1 + jd * a_dim1;
i__3 = jd + 1 + jd * a_dim1;
d__1 = *amagn * a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
/* L240: */
}
/* If RSIGN = .TRUE., assign random signs to diagonal and */
/* subdiagonal */
if (*rsign) {
i__1 = kend;
for (jd = kbeg; jd <= i__1; ++jd) {
i__2 = jd + jd * a_dim1;
if (a[i__2].r != 0.) {
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
d__1 = z_abs(&ctemp);
z__1.r = ctemp.r / d__1, z__1.i = ctemp.i / d__1;
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = jd + jd * a_dim1;
i__3 = jd + jd * a_dim1;
d__1 = a[i__3].r;
z__1.r = d__1 * ctemp.r, z__1.i = d__1 * ctemp.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
}
/* L250: */
}
i__1 = isde;
for (jd = isdb; jd <= i__1; ++jd) {
i__2 = jd + 1 + jd * a_dim1;
if (a[i__2].r != 0.) {
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
d__1 = z_abs(&ctemp);
z__1.r = ctemp.r / d__1, z__1.i = ctemp.i / d__1;
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = jd + 1 + jd * a_dim1;
i__3 = jd + 1 + jd * a_dim1;
d__1 = a[i__3].r;
z__1.r = d__1 * ctemp.r, z__1.i = d__1 * ctemp.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
}
/* L260: */
}
}
/* Reverse if ITYPE < 0 */
if (*itype < 0) {
i__1 = (kbeg + kend - 1) / 2;
for (jd = kbeg; jd <= i__1; ++jd) {
i__2 = jd + jd * a_dim1;
ctemp.r = a[i__2].r, ctemp.i = a[i__2].i;
i__2 = jd + jd * a_dim1;
i__3 = kbeg + kend - jd + (kbeg + kend - jd) * a_dim1;
a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i;
i__2 = kbeg + kend - jd + (kbeg + kend - jd) * a_dim1;
a[i__2].r = ctemp.r, a[i__2].i = ctemp.i;
/* L270: */
}
i__1 = (*n - 1) / 2;
for (jd = 1; jd <= i__1; ++jd) {
i__2 = jd + 1 + jd * a_dim1;
ctemp.r = a[i__2].r, ctemp.i = a[i__2].i;
i__2 = jd + 1 + jd * a_dim1;
i__3 = *n + 1 - jd + (*n - jd) * a_dim1;
a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i;
i__2 = *n + 1 - jd + (*n - jd) * a_dim1;
a[i__2].r = ctemp.r, a[i__2].i = ctemp.i;
/* L280: */
}
}
}
/* Fill in upper triangle */
if (*triang != 0.) {
i__1 = *n;
for (jc = 2; jc <= i__1; ++jc) {
i__2 = jc - 1;
for (jr = 1; jr <= i__2; ++jr) {
i__3 = jr + jc * a_dim1;
zlarnd_(&z__2, idist, &iseed[1]);
z__1.r = *triang * z__2.r, z__1.i = *triang * z__2.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L290: */
}
/* L300: */
}
}
return 0;
/* End of ZLATM4 */
} /* zlatm4_ */
/* Subroutine */ int zlatm1_(integer *mode, doublereal *cond, integer *irsign,
integer *idist, integer *iseed, doublecomplex *d__, integer *n,
integer *info)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublereal d__1;
doublecomplex z__1, z__2;
/* Local variables */
integer i__;
doublereal temp, alpha;
doublecomplex ctemp;
extern doublereal dlaran_(integer *);
extern /* Double Complex */ void zlarnd_(doublecomplex *, integer *,
integer *);
extern /* Subroutine */ int zlarnv_(integer *, integer *, integer *,
doublecomplex *);
/* -- LAPACK auxiliary test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLATM1 computes the entries of D(1..N) as specified by */
/* MODE, COND and IRSIGN. IDIST and ISEED determine the generation */
/* of random numbers. ZLATM1 is called by CLATMR to generate */
/* random test matrices for LAPACK programs. */
/* Arguments */
/* ========= */
/* MODE - INTEGER */
/* On entry describes how D is to be computed: */
/* MODE = 0 means do not change D. */
/* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND */
/* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND */
/* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) */
/* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) */
/* MODE = 5 sets D to random numbers in the range */
/* ( 1/COND , 1 ) such that their logarithms */
/* are uniformly distributed. */
/* MODE = 6 set D to random numbers from same distribution */
/* as the rest of the matrix. */
/* MODE < 0 has the same meaning as ABS(MODE), except that */
/* the order of the elements of D is reversed. */
/* Thus if MODE is positive, D has entries ranging from */
/* 1 to 1/COND, if negative, from 1/COND to 1, */
/* Not modified. */
/* COND - DOUBLE PRECISION */
/* On entry, used as described under MODE above. */
/* If used, it must be >= 1. Not modified. */
/* IRSIGN - INTEGER */
/* On entry, if MODE neither -6, 0 nor 6, determines sign of */
/* entries of D */
/* 0 => leave entries of D unchanged */
/* 1 => multiply each entry of D by random complex number */
/* uniformly distributed with absolute value 1 */
/* IDIST - CHARACTER*1 */
/* On entry, IDIST specifies the type of distribution to be */
/* used to generate a random matrix . */
/* 1 => real and imaginary parts each UNIFORM( 0, 1 ) */
/* 2 => real and imaginary parts each UNIFORM( -1, 1 ) */
/* 3 => real and imaginary parts each NORMAL( 0, 1 ) */
/* 4 => complex number uniform in DISK( 0, 1 ) */
/* Not modified. */
/* ISEED - INTEGER array, dimension ( 4 ) */
/* On entry ISEED specifies the seed of the random number */
/* generator. 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 ZLATM1 */
/* to continue the same random number sequence. */
/* Changed on exit. */
/* D - COMPLEX*16 array, dimension ( MIN( M , N ) ) */
/* Array to be computed according to MODE, COND and IRSIGN. */
/* May be changed on exit if MODE is nonzero. */
/* N - INTEGER */
/* Number of entries of D. Not modified. */
/* INFO - INTEGER */
/* 0 => normal termination */
/* -1 => if MODE not in range -6 to 6 */
/* -2 => if MODE neither -6, 0 nor 6, and */
/* IRSIGN neither 0 nor 1 */
/* -3 => if MODE neither -6, 0 nor 6 and COND less than 1 */
/* -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 4 */
/* -7 => if N negative */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode and Test the input parameters. Initialize flags & seed. */
/* Parameter adjustments */
--d__;
--iseed;
/* Function Body */
*info = 0;
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Set INFO if an error */
if (*mode < -6 || *mode > 6) {
*info = -1;
} else if (*mode != -6 && *mode != 0 && *mode != 6 && (*irsign != 0 && *
irsign != 1)) {
*info = -2;
} else if (*mode != -6 && *mode != 0 && *mode != 6 && *cond < 1.) {
*info = -3;
} else if ((*mode == 6 || *mode == -6) && (*idist < 1 || *idist > 4)) {
*info = -4;
} else if (*n < 0) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZLATM1", &i__1);
return 0;
}
/* Compute D according to COND and MODE */
if (*mode != 0) {
switch (abs(*mode)) {
case 1: goto L10;
case 2: goto L30;
case 3: goto L50;
case 4: goto L70;
case 5: goto L90;
case 6: goto L110;
}
/* One large D value: */
L10:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
d__1 = 1. / *cond;
d__[i__2].r = d__1, d__[i__2].i = 0.;
/* L20: */
}
d__[1].r = 1., d__[1].i = 0.;
goto L120;
/* One small D value: */
L30:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
d__[i__2].r = 1., d__[i__2].i = 0.;
/* L40: */
}
i__1 = *n;
d__1 = 1. / *cond;
d__[i__1].r = d__1, d__[i__1].i = 0.;
goto L120;
/* Exponentially distributed D values: */
L50:
d__[1].r = 1., d__[1].i = 0.;
if (*n > 1) {
d__1 = -1. / (doublereal) (*n - 1);
alpha = pow_dd(cond, &d__1);
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__ - 1;
d__1 = pow_di(&alpha, &i__3);
d__[i__2].r = d__1, d__[i__2].i = 0.;
/* L60: */
}
}
goto L120;
/* Arithmetically distributed D values: */
L70:
d__[1].r = 1., d__[1].i = 0.;
if (*n > 1) {
temp = 1. / *cond;
alpha = (1. - temp) / (doublereal) (*n - 1);
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
i__2 = i__;
d__1 = (doublereal) (*n - i__) * alpha + temp;
d__[i__2].r = d__1, d__[i__2].i = 0.;
/* L80: */
}
}
goto L120;
/* Randomly distributed D values on ( 1/COND , 1): */
L90:
alpha = log(1. / *cond);
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
d__1 = exp(alpha * dlaran_(&iseed[1]));
d__[i__2].r = d__1, d__[i__2].i = 0.;
/* L100: */
}
goto L120;
/* Randomly distributed D values from IDIST */
L110:
zlarnv_(idist, &iseed[1], n, &d__[1]);
L120:
/* If MODE neither -6 nor 0 nor 6, and IRSIGN = 1, assign */
/* random signs to D */
if (*mode != -6 && *mode != 0 && *mode != 6 && *irsign == 1) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = i__;
i__3 = i__;
d__1 = z_abs(&ctemp);
z__2.r = ctemp.r / d__1, z__2.i = ctemp.i / d__1;
z__1.r = d__[i__3].r * z__2.r - d__[i__3].i * z__2.i, z__1.i =
d__[i__3].r * z__2.i + d__[i__3].i * z__2.r;
d__[i__2].r = z__1.r, d__[i__2].i = z__1.i;
/* L130: */
}
}
/* Reverse if MODE < 0 */
if (*mode < 0) {
i__1 = *n / 2;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
ctemp.r = d__[i__2].r, ctemp.i = d__[i__2].i;
i__2 = i__;
i__3 = *n + 1 - i__;
d__[i__2].r = d__[i__3].r, d__[i__2].i = d__[i__3].i;
i__2 = *n + 1 - i__;
d__[i__2].r = ctemp.r, d__[i__2].i = ctemp.i;
/* L140: */
}
}
}
return 0;
/* End of ZLATM1 */
} /* zlatm1_ */
/* Subroutine */ int zdrvrf4_(integer *nout, integer *nn, integer *nval,
doublereal *thresh, doublecomplex *c1, doublecomplex *c2, integer *
ldc, doublecomplex *crf, doublecomplex *a, integer *lda, doublereal *
d_work_zlange__)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char uplos[1*2] = "U" "L";
static char forms[1*2] = "N" "C";
static char transs[1*2] = "N" "C";
/* Format strings */
static char fmt_9999[] = "(1x,\002 *** Error(s) or Failure(s) while test"
"ing ZHFRK ***\002)";
static char fmt_9997[] = "(1x,\002 Failure in \002,a5,\002, CFORM="
"'\002,a1,\002',\002,\002 UPLO='\002,a1,\002',\002,\002 TRANS="
"'\002,a1,\002',\002,\002 N=\002,i3,\002, K =\002,i3,\002, test"
"=\002,g12.5)";
static char fmt_9996[] = "(1x,\002All tests for \002,a5,\002 auxiliary r"
"outine passed the \002,\002threshold (\002,i5,\002 tests run)"
"\002)";
static char fmt_9995[] = "(1x,a6,\002 auxiliary routine:\002,i5,\002 out"
" of \002,i5,\002 tests failed to pass the threshold\002)";
/* System generated locals */
integer a_dim1, a_offset, c1_dim1, c1_offset, c2_dim1, c2_offset, i__1,
i__2, i__3, i__4, i__5, i__6, i__7;
doublereal d__1;
doublecomplex z__1;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsle(cilist *), e_wsle(void), s_wsfe(cilist *), e_wsfe(void),
do_fio(integer *, char *, ftnlen);
/* Local variables */
integer i__, j, k, n, iik, iin;
doublereal eps, beta;
integer info;
char uplo[1];
integer nrun;
doublereal alpha;
integer nfail, iseed[4];
char cform[1];
integer iform;
doublereal norma, normc;
extern /* Subroutine */ int zherk_(char *, char *, integer *, integer *,
doublereal *, doublecomplex *, integer *, doublereal *,
doublecomplex *, integer *), zhfrk_(char *, char *
, char *, integer *, integer *, doublereal *, doublecomplex *,
integer *, doublereal *, doublecomplex *);
char trans[1];
integer iuplo;
extern doublereal dlamch_(char *);
integer ialpha;
extern doublereal dlarnd_(integer *, integer *), zlange_(char *, integer *
, integer *, doublecomplex *, integer *, doublereal *);
extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *,
integer *);
integer itrans;
doublereal result[1];
extern /* Subroutine */ int ztfttr_(char *, char *, integer *,
doublecomplex *, doublecomplex *, integer *, integer *), ztrttf_(char *, char *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *);
/* Fortran I/O blocks */
static cilist io___28 = { 0, 0, 0, 0, 0 };
static cilist io___29 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___30 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___31 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___32 = { 0, 0, 0, fmt_9995, 0 };
/* -- LAPACK test routine (version 3.2.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2008 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZDRVRF4 tests the LAPACK RFP routines: */
/* ZHFRK */
/* Arguments */
/* ========= */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix dimension N. */
/* THRESH (input) DOUBLE PRECISION */
/* 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. */
/* C1 (workspace) COMPLEX*16 array, dimension (LDC,NMAX) */
/* C2 (workspace) COMPLEX*16 array, dimension (LDC,NMAX) */
/* LDC (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,NMAX). */
/* CRF (workspace) COMPLEX*16 array, dimension ((NMAX*(NMAX+1))/2). */
/* A (workspace) COMPLEX*16 array, dimension (LDA,NMAX) */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,NMAX). */
/* D_WORK_ZLANGE (workspace) DOUBLE PRECISION array, dimension (NMAX) */
/* ===================================================================== */
/* .. */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--nval;
c2_dim1 = *ldc;
c2_offset = 1 + c2_dim1;
c2 -= c2_offset;
c1_dim1 = *ldc;
c1_offset = 1 + c1_dim1;
c1 -= c1_offset;
--crf;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--d_work_zlange__;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
nrun = 0;
nfail = 0;
info = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
eps = dlamch_("Precision");
i__1 = *nn;
for (iin = 1; iin <= i__1; ++iin) {
n = nval[iin];
i__2 = *nn;
for (iik = 1; iik <= i__2; ++iik) {
k = nval[iin];
for (iform = 1; iform <= 2; ++iform) {
*(unsigned char *)cform = *(unsigned char *)&forms[iform - 1];
for (iuplo = 1; iuplo <= 2; ++iuplo) {
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo -
1];
for (itrans = 1; itrans <= 2; ++itrans) {
*(unsigned char *)trans = *(unsigned char *)&transs[
itrans - 1];
for (ialpha = 1; ialpha <= 4; ++ialpha) {
if (ialpha == 1) {
alpha = 0.;
beta = 0.;
} else if (ialpha == 1) {
alpha = 1.;
beta = 0.;
} else if (ialpha == 1) {
alpha = 0.;
beta = 1.;
} else {
alpha = dlarnd_(&c__2, iseed);
beta = dlarnd_(&c__2, iseed);
}
/* All the parameters are set: */
/* CFORM, UPLO, TRANS, M, N, */
/* ALPHA, and BETA */
/* READY TO TEST! */
++nrun;
if (itrans == 1) {
/* In this case we are NOTRANS, so A is N-by-K */
i__3 = k;
for (j = 1; j <= i__3; ++j) {
i__4 = n;
for (i__ = 1; i__ <= i__4; ++i__) {
i__5 = i__ + j * a_dim1;
zlarnd_(&z__1, &c__4, iseed);
a[i__5].r = z__1.r, a[i__5].i =
z__1.i;
}
}
norma = zlange_("I", &n, &k, &a[a_offset],
lda, &d_work_zlange__[1]);
} else {
/* In this case we are TRANS, so A is K-by-N */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = k;
for (i__ = 1; i__ <= i__4; ++i__) {
i__5 = i__ + j * a_dim1;
zlarnd_(&z__1, &c__4, iseed);
a[i__5].r = z__1.r, a[i__5].i =
z__1.i;
}
}
norma = zlange_("I", &k, &n, &a[a_offset],
lda, &d_work_zlange__[1]);
}
/* Generate C1 our N--by--N Hermitian matrix. */
/* Make sure C2 has the same upper/lower part, */
/* (the one that we do not touch), so */
/* copy the initial C1 in C2 in it. */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = n;
for (i__ = 1; i__ <= i__4; ++i__) {
i__5 = i__ + j * c1_dim1;
zlarnd_(&z__1, &c__4, iseed);
c1[i__5].r = z__1.r, c1[i__5].i = z__1.i;
i__5 = i__ + j * c2_dim1;
i__6 = i__ + j * c1_dim1;
c2[i__5].r = c1[i__6].r, c2[i__5].i = c1[
i__6].i;
}
}
/* (See comment later on for why we use ZLANGE and */
/* not ZLANHE for C1.) */
normc = zlange_("I", &n, &n, &c1[c1_offset], ldc,
&d_work_zlange__[1]);
s_copy(srnamc_1.srnamt, "ZTRTTF", (ftnlen)32, (
ftnlen)6);
ztrttf_(cform, uplo, &n, &c1[c1_offset], ldc, &
crf[1], &info);
/* call zherk the BLAS routine -> gives C1 */
s_copy(srnamc_1.srnamt, "ZHERK ", (ftnlen)32, (
ftnlen)6);
zherk_(uplo, trans, &n, &k, &alpha, &a[a_offset],
lda, &beta, &c1[c1_offset], ldc);
/* call zhfrk the RFP routine -> gives CRF */
s_copy(srnamc_1.srnamt, "ZHFRK ", (ftnlen)32, (
ftnlen)6);
zhfrk_(cform, uplo, trans, &n, &k, &alpha, &a[
a_offset], lda, &beta, &crf[1]);
/* convert CRF in full format -> gives C2 */
s_copy(srnamc_1.srnamt, "ZTFTTR", (ftnlen)32, (
ftnlen)6);
ztfttr_(cform, uplo, &n, &crf[1], &c2[c2_offset],
ldc, &info);
/* compare C1 and C2 */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = n;
for (i__ = 1; i__ <= i__4; ++i__) {
i__5 = i__ + j * c1_dim1;
i__6 = i__ + j * c1_dim1;
i__7 = i__ + j * c2_dim1;
z__1.r = c1[i__6].r - c2[i__7].r, z__1.i =
c1[i__6].i - c2[i__7].i;
c1[i__5].r = z__1.r, c1[i__5].i = z__1.i;
}
}
/* Yes, C1 is Hermitian so we could call ZLANHE, */
/* but we want to check the upper part that is */
/* supposed to be unchanged and the diagonal that */
/* is supposed to be real -> ZLANGE */
result[0] = zlange_("I", &n, &n, &c1[c1_offset],
ldc, &d_work_zlange__[1]);
/* Computing MAX */
d__1 = abs(alpha) * norma * norma + abs(beta) *
normc;
result[0] = result[0] / max(d__1,1.) / max(n,1) /
eps;
if (result[0] >= *thresh) {
if (nfail == 0) {
io___28.ciunit = *nout;
s_wsle(&io___28);
e_wsle();
io___29.ciunit = *nout;
s_wsfe(&io___29);
e_wsfe();
}
io___30.ciunit = *nout;
s_wsfe(&io___30);
do_fio(&c__1, "ZHFRK", (ftnlen)5);
do_fio(&c__1, cform, (ftnlen)1);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[0], (ftnlen)
sizeof(doublereal));
e_wsfe();
++nfail;
}
/* L100: */
}
/* L110: */
}
/* L120: */
}
/* L130: */
}
/* L140: */
}
/* L150: */
}
/* Print a summary of the results. */
if (nfail == 0) {
io___31.ciunit = *nout;
s_wsfe(&io___31);
do_fio(&c__1, "ZHFRK", (ftnlen)5);
do_fio(&c__1, (char *)&nrun, (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___32.ciunit = *nout;
s_wsfe(&io___32);
do_fio(&c__1, "ZHFRK", (ftnlen)5);
do_fio(&c__1, (char *)&nfail, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nrun, (ftnlen)sizeof(integer));
e_wsfe();
}
return 0;
/* End of ZDRVRF4 */
} /* zdrvrf4_ */
/* Double Complex */ void zlatm2_(doublecomplex * ret_val, integer *m,
integer *n, integer *i__, integer *j, integer *kl, integer *ku,
integer *idist, integer *iseed, doublecomplex *d__, integer *igrade,
doublecomplex *dl, doublecomplex *dr, integer *ipvtng, integer *iwork,
doublereal *sparse)
{
/* System generated locals */
integer i__1, i__2;
doublecomplex z__1, z__2, z__3;
/* Local variables */
integer isub, jsub;
doublecomplex ctemp;
extern doublereal dlaran_(integer *);
extern /* Double Complex */ void zlarnd_(doublecomplex *, integer *,
integer *);
/* -- LAPACK auxiliary test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLATM2 returns the (I,J) entry of a random matrix of dimension */
/* (M, N) described by the other paramters. It is called by the */
/* ZLATMR routine in order to build random test matrices. No error */
/* checking on parameters is done, because this routine is called in */
/* a tight loop by ZLATMR which has already checked the parameters. */
/* Use of ZLATM2 differs from CLATM3 in the order in which the random */
/* number generator is called to fill in random matrix entries. */
/* With ZLATM2, the generator is called to fill in the pivoted matrix */
/* columnwise. With ZLATM3, the generator is called to fill in the */
/* matrix columnwise, after which it is pivoted. Thus, ZLATM3 can */
/* be used to construct random matrices which differ only in their */
/* order of rows and/or columns. ZLATM2 is used to construct band */
/* matrices while avoiding calling the random number generator for */
/* entries outside the band (and therefore generating random numbers */
/* The matrix whose (I,J) entry is returned is constructed as */
/* follows (this routine only computes one entry): */
/* If I is outside (1..M) or J is outside (1..N), return zero */
/* (this is convenient for generating matrices in band format). */
/* Generate a matrix A with random entries of distribution IDIST. */
/* Set the diagonal to D. */
/* Grade the matrix, if desired, from the left (by DL) and/or */
/* from the right (by DR or DL) as specified by IGRADE. */
/* Permute, if desired, the rows and/or columns as specified by */
/* IPVTNG and IWORK. */
/* Band the matrix to have lower bandwidth KL and upper */
/* bandwidth KU. */
/* Set random entries to zero as specified by SPARSE. */
/* Arguments */
/* ========= */
/* M - INTEGER */
/* Number of rows of matrix. Not modified. */
/* N - INTEGER */
/* Number of columns of matrix. Not modified. */
/* I - INTEGER */
/* Row of entry to be returned. Not modified. */
/* J - INTEGER */
/* Column of entry to be returned. Not modified. */
/* KL - INTEGER */
/* Lower bandwidth. Not modified. */
/* KU - INTEGER */
/* Upper bandwidth. Not modified. */
/* IDIST - INTEGER */
/* On entry, IDIST specifies the type of distribution to be */
/* used to generate a random matrix . */
/* 1 => real and imaginary parts each UNIFORM( 0, 1 ) */
/* 2 => real and imaginary parts each UNIFORM( -1, 1 ) */
/* 3 => real and imaginary parts each NORMAL( 0, 1 ) */
/* 4 => complex number uniform in DISK( 0 , 1 ) */
/* Not modified. */
/* ISEED - INTEGER array of dimension ( 4 ) */
/* Seed for random number generator. */
/* Changed on exit. */
/* D - COMPLEX*16 array of dimension ( MIN( I , J ) ) */
/* Diagonal entries of matrix. Not modified. */
/* IGRADE - INTEGER */
/* Specifies grading of matrix as follows: */
/* 0 => no grading */
/* 1 => matrix premultiplied by diag( DL ) */
/* 2 => matrix postmultiplied by diag( DR ) */
/* 3 => matrix premultiplied by diag( DL ) and */
/* postmultiplied by diag( DR ) */
/* 4 => matrix premultiplied by diag( DL ) and */
/* postmultiplied by inv( diag( DL ) ) */
/* 5 => matrix premultiplied by diag( DL ) and */
/* postmultiplied by diag( CONJG(DL) ) */
/* 6 => matrix premultiplied by diag( DL ) and */
/* postmultiplied by diag( DL ) */
/* Not modified. */
/* DL - COMPLEX*16 array ( I or J, as appropriate ) */
/* Left scale factors for grading matrix. Not modified. */
/* DR - COMPLEX*16 array ( I or J, as appropriate ) */
/* Right scale factors for grading matrix. Not modified. */
/* IPVTNG - INTEGER */
/* On entry specifies pivoting permutations as follows: */
/* 0 => none. */
/* 1 => row pivoting. */
/* 2 => column pivoting. */
/* 3 => full pivoting, i.e., on both sides. */
/* Not modified. */
/* IWORK - INTEGER array ( I or J, as appropriate ) */
/* This array specifies the permutation used. The */
/* row (or column) in position K was originally in */
/* position IWORK( K ). */
/* This differs from IWORK for ZLATM3. Not modified. */
/* SPARSE - DOUBLE PRECISION between 0. and 1. */
/* On entry specifies the sparsity of the matrix */
/* if sparse matix is to be generated. */
/* SPARSE should lie between 0 and 1. */
/* A uniform ( 0, 1 ) random number x is generated and */
/* compared to SPARSE; if x is larger the matrix entry */
/* is unchanged and if x is smaller the entry is set */
/* to zero. Thus on the average a fraction SPARSE of the */
/* entries will be set to zero. */
/* Not modified. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* ----------------------------------------------------------------------- */
/* .. Executable Statements .. */
/* Check for I and J in range */
/* Parameter adjustments */
--iwork;
--dr;
--dl;
--d__;
--iseed;
/* Function Body */
if (*i__ < 1 || *i__ > *m || *j < 1 || *j > *n) {
ret_val->r = 0., ret_val->i = 0.;
return ;
}
/* Check for banding */
if (*j > *i__ + *ku || *j < *i__ - *kl) {
ret_val->r = 0., ret_val->i = 0.;
return ;
}
/* Check for sparsity */
if (*sparse > 0.) {
if (dlaran_(&iseed[1]) < *sparse) {
ret_val->r = 0., ret_val->i = 0.;
return ;
}
}
/* Compute subscripts depending on IPVTNG */
if (*ipvtng == 0) {
isub = *i__;
jsub = *j;
} else if (*ipvtng == 1) {
isub = iwork[*i__];
jsub = *j;
} else if (*ipvtng == 2) {
isub = *i__;
jsub = iwork[*j];
} else if (*ipvtng == 3) {
isub = iwork[*i__];
jsub = iwork[*j];
}
/* Compute entry and grade it according to IGRADE */
if (isub == jsub) {
i__1 = isub;
ctemp.r = d__[i__1].r, ctemp.i = d__[i__1].i;
} else {
zlarnd_(&z__1, idist, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
}
if (*igrade == 1) {
i__1 = isub;
z__1.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__1.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 2) {
i__1 = jsub;
z__1.r = ctemp.r * dr[i__1].r - ctemp.i * dr[i__1].i, z__1.i =
ctemp.r * dr[i__1].i + ctemp.i * dr[i__1].r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 3) {
i__1 = isub;
z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
i__2 = jsub;
z__1.r = z__2.r * dr[i__2].r - z__2.i * dr[i__2].i, z__1.i = z__2.r *
dr[i__2].i + z__2.i * dr[i__2].r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 4 && isub != jsub) {
i__1 = isub;
z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
z_div(&z__1, &z__2, &dl[jsub]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 5) {
i__1 = isub;
z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
d_cnjg(&z__3, &dl[jsub]);
z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i
+ z__2.i * z__3.r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 6) {
i__1 = isub;
z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
i__2 = jsub;
z__1.r = z__2.r * dl[i__2].r - z__2.i * dl[i__2].i, z__1.i = z__2.r *
dl[i__2].i + z__2.i * dl[i__2].r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
}
ret_val->r = ctemp.r, ret_val->i = ctemp.i;
return ;
/* End of ZLATM2 */
} /* zlatm2_ */
/* Subroutine */ int zdrvrf1_(integer *nout, integer *nn, integer *nval,
doublereal *thresh, doublecomplex *a, integer *lda, doublecomplex *
arf, doublereal *work)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char uplos[1*2] = "U" "L";
static char forms[1*2] = "N" "C";
static char norms[1*4] = "M" "1" "I" "F";
/* Format strings */
static char fmt_9999[] = "(1x,\002 *** Error(s) or Failure(s) while test"
"ing ZLANHF ***\002)";
static char fmt_9998[] = "(1x,\002 Error in \002,a6,\002 with UPLO="
"'\002,a1,\002', FORM='\002,a1,\002', N=\002,i5)";
static char fmt_9997[] = "(1x,\002 Failure in \002,a6,\002 N=\002,"
"i5,\002 TYPE=\002,i5,\002 UPLO='\002,a1,\002', FORM ='\002,a1"
",\002', NORM='\002,a1,\002', test=\002,g12.5)";
static char fmt_9996[] = "(1x,\002All tests for \002,a6,\002 auxiliary r"
"outine passed the \002,\002threshold (\002,i5,\002 tests run)"
"\002)";
static char fmt_9995[] = "(1x,a6,\002 auxiliary routine:\002,i5,\002 out"
" of \002,i5,\002 tests failed to pass the threshold\002)";
static char fmt_9994[] = "(26x,i5,\002 error message recorded (\002,a6"
",\002)\002)";
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsle(cilist *), e_wsle(void), s_wsfe(cilist *), e_wsfe(void),
do_fio(integer *, char *, ftnlen);
/* Local variables */
integer i__, j, n, iin, iit;
doublereal eps;
integer info;
char norm[1], uplo[1];
integer nrun, nfail;
doublereal large;
integer iseed[4];
char cform[1];
doublereal small;
integer iform;
doublereal norma;
integer inorm, iuplo, nerrs;
extern doublereal dlamch_(char *), zlanhe_(char *, char *,
integer *, doublecomplex *, integer *, doublereal *), zlanhf_(char *, char *, char *, integer *, doublecomplex
*, doublereal *);
extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *,
integer *);
doublereal result[1];
extern /* Subroutine */ int ztrttf_(char *, char *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
doublereal normarf;
/* Fortran I/O blocks */
static cilist io___22 = { 0, 0, 0, 0, 0 };
static cilist io___23 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___24 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___30 = { 0, 0, 0, 0, 0 };
static cilist io___31 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___32 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___33 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___34 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___35 = { 0, 0, 0, fmt_9994, 0 };
/* -- LAPACK test routine (version 3.2.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2008 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZDRVRF1 tests the LAPACK RFP routines: */
/* ZLANHF.F */
/* Arguments */
/* ========= */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix dimension N. */
/* THRESH (input) DOUBLE PRECISION */
/* 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. */
/* A (workspace) COMPLEX*16 array, dimension (LDA,NMAX) */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,NMAX). */
/* ARF (workspace) COMPLEX*16 array, dimension ((NMAX*(NMAX+1))/2). */
/* WORK (workspace) DOUBLE PRECISION array, dimension ( NMAX ) */
/* ===================================================================== */
/* .. */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--nval;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--arf;
--work;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
nrun = 0;
nfail = 0;
nerrs = 0;
info = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
eps = dlamch_("Precision");
small = dlamch_("Safe minimum");
large = 1. / small;
small = small * *lda * *lda;
large = large / *lda / *lda;
i__1 = *nn;
for (iin = 1; iin <= i__1; ++iin) {
n = nval[iin];
for (iit = 1; iit <= 3; ++iit) {
/* IIT = 1 : random matrix */
/* IIT = 2 : random matrix scaled near underflow */
/* IIT = 3 : random matrix scaled near overflow */
i__2 = n;
for (j = 1; j <= i__2; ++j) {
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * a_dim1;
zlarnd_(&z__1, &c__4, iseed);
a[i__4].r = z__1.r, a[i__4].i = z__1.i;
}
}
if (iit == 2) {
i__2 = n;
for (j = 1; j <= i__2; ++j) {
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * a_dim1;
i__5 = i__ + j * a_dim1;
z__1.r = large * a[i__5].r, z__1.i = large * a[i__5]
.i;
a[i__4].r = z__1.r, a[i__4].i = z__1.i;
}
}
}
if (iit == 3) {
i__2 = n;
for (j = 1; j <= i__2; ++j) {
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * a_dim1;
i__5 = i__ + j * a_dim1;
z__1.r = small * a[i__5].r, z__1.i = small * a[i__5]
.i;
a[i__4].r = z__1.r, a[i__4].i = z__1.i;
}
}
}
/* Do first for UPLO = 'U', then for UPLO = 'L' */
for (iuplo = 1; iuplo <= 2; ++iuplo) {
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
/* Do first for CFORM = 'N', then for CFORM = 'C' */
for (iform = 1; iform <= 2; ++iform) {
*(unsigned char *)cform = *(unsigned char *)&forms[iform
- 1];
s_copy(srnamc_1.srnamt, "ZTRTTF", (ftnlen)32, (ftnlen)6);
ztrttf_(cform, uplo, &n, &a[a_offset], lda, &arf[1], &
info);
/* Check error code from ZTRTTF */
if (info != 0) {
if (nfail == 0 && nerrs == 0) {
io___22.ciunit = *nout;
s_wsle(&io___22);
e_wsle();
io___23.ciunit = *nout;
s_wsfe(&io___23);
e_wsfe();
}
io___24.ciunit = *nout;
s_wsfe(&io___24);
do_fio(&c__1, srnamc_1.srnamt, (ftnlen)32);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, cform, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
e_wsfe();
++nerrs;
goto L100;
}
for (inorm = 1; inorm <= 4; ++inorm) {
/* Check all four norms: 'M', '1', 'I', 'F' */
*(unsigned char *)norm = *(unsigned char *)&norms[
inorm - 1];
normarf = zlanhf_(norm, cform, uplo, &n, &arf[1], &
work[1]);
norma = zlanhe_(norm, uplo, &n, &a[a_offset], lda, &
work[1]);
result[0] = (norma - normarf) / norma / eps;
++nrun;
if (result[0] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
io___30.ciunit = *nout;
s_wsle(&io___30);
e_wsle();
io___31.ciunit = *nout;
s_wsfe(&io___31);
e_wsfe();
}
io___32.ciunit = *nout;
s_wsfe(&io___32);
do_fio(&c__1, "ZLANHF", (ftnlen)6);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&iit, (ftnlen)sizeof(
integer));
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, cform, (ftnlen)1);
do_fio(&c__1, norm, (ftnlen)1);
do_fio(&c__1, (char *)&result[0], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
/* L90: */
}
L100:
;
}
/* L110: */
}
/* L120: */
}
/* L130: */
}
/* Print a summary of the results. */
if (nfail == 0) {
io___33.ciunit = *nout;
s_wsfe(&io___33);
do_fio(&c__1, "ZLANHF", (ftnlen)6);
do_fio(&c__1, (char *)&nrun, (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___34.ciunit = *nout;
s_wsfe(&io___34);
do_fio(&c__1, "ZLANHF", (ftnlen)6);
do_fio(&c__1, (char *)&nfail, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nrun, (ftnlen)sizeof(integer));
e_wsfe();
}
if (nerrs != 0) {
io___35.ciunit = *nout;
s_wsfe(&io___35);
do_fio(&c__1, (char *)&nerrs, (ftnlen)sizeof(integer));
do_fio(&c__1, "ZLANHF", (ftnlen)6);
e_wsfe();
}
return 0;
/* End of ZDRVRF1 */
} /* zdrvrf1_ */
/* Subroutine */ int zlatme_(integer *n, char *dist, integer *iseed,
doublecomplex *d, integer *mode, doublereal *cond, doublecomplex *
dmax__, char *ei, char *rsign, char *upper, char *sim, doublereal *ds,
integer *modes, doublereal *conds, integer *kl, integer *ku,
doublereal *anorm, doublecomplex *a, integer *lda, doublecomplex *
work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
doublereal d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions */
double z_abs(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static logical bads;
static integer isim;
static doublereal temp;
static integer i, j;
static doublecomplex alpha;
extern logical lsame_(char *, char *);
static integer iinfo;
static doublereal tempa[1];
static integer icols;
extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static integer idist;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *), zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
static integer irows;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), dlatm1_(integer *, doublereal *,
integer *, integer *, integer *, doublereal *, integer *, integer
*), zlatm1_(integer *, doublereal *, integer *, integer *,
integer *, doublecomplex *, integer *, integer *);
static integer ic, jc, ir;
static doublereal ralpha;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *), zlarge_(integer *, doublecomplex *,
integer *, integer *, doublecomplex *, integer *), zlarfg_(
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *), zlacgv_(integer *, doublecomplex *, integer *);
extern /* Double Complex */ void zlarnd_(doublecomplex *, integer *,
integer *);
static integer irsign;
extern /* Subroutine */ int zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *);
static integer iupper;
extern /* Subroutine */ int zlarnv_(integer *, integer *, integer *,
doublecomplex *);
static doublecomplex xnorms;
static integer jcr;
static doublecomplex tau;
/* -- LAPACK test routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZLATME generates random non-symmetric square matrices with
specified eigenvalues for testing LAPACK programs.
ZLATME operates by applying the following sequence of
operations:
1. Set the diagonal to D, where D may be input or
computed according to MODE, COND, DMAX, and RSIGN
as described below.
2. If UPPER='T', the upper triangle of A is set to random values
out of distribution DIST.
3. If SIM='T', A is multiplied on the left by a random matrix
X, whose singular values are specified by DS, MODES, and
CONDS, and on the right by X inverse.
4. If KL < N-1, the lower bandwidth is reduced to KL using
Householder transformations. If KU < N-1, the upper
bandwidth is reduced to KU.
5. If ANORM is not negative, the matrix is scaled to have
maximum-element-norm ANORM.
(Note: since the matrix cannot be reduced beyond Hessenberg form,
no packing options are available.)
Arguments
=========
N - INTEGER
The number of columns (or rows) of A. Not modified.
DIST - CHARACTER*1
On entry, DIST specifies the type of distribution to be used
to generate the random eigen-/singular values, and on the
upper triangle (see UPPER).
'U' => UNIFORM( 0, 1 ) ( 'U' for uniform )
'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric )
'N' => NORMAL( 0, 1 ) ( 'N' for normal )
'D' => uniform on the complex disc |z| < 1.
Not modified.
ISEED - INTEGER array, dimension ( 4 )
On entry ISEED specifies the seed of the random number
generator. They should lie between 0 and 4095 inclusive,
and ISEED(4) should 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 ZLATME
to continue the same random number sequence.
Changed on exit.
D - COMPLEX*16 array, dimension ( N )
This array is used to specify the eigenvalues of A. If
MODE=0, then D is assumed to contain the eigenvalues
otherwise they will be computed according to MODE, COND,
DMAX, and RSIGN and placed in D.
Modified if MODE is nonzero.
MODE - INTEGER
On entry this describes how the eigenvalues are to
be specified:
MODE = 0 means use D as input
MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND
MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND
MODE = 3 sets D(I)=COND**(-(I-1)/(N-1))
MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
MODE = 5 sets D to random numbers in the range
( 1/COND , 1 ) such that their logarithms
are uniformly distributed.
MODE = 6 set D to random numbers from same distribution
as the rest of the matrix.
MODE < 0 has the same meaning as ABS(MODE), except that
the order of the elements of D is reversed.
Thus if MODE is between 1 and 4, D has entries ranging
from 1 to 1/COND, if between -1 and -4, D has entries
ranging from 1/COND to 1,
Not modified.
COND - DOUBLE PRECISION
On entry, this is used as described under MODE above.
If used, it must be >= 1. Not modified.
DMAX - COMPLEX*16
If MODE is neither -6, 0 nor 6, the contents of D, as
computed according to MODE and COND, will be scaled by
DMAX / max(abs(D(i))). Note that DMAX need not be
positive or real: if DMAX is negative or complex (or zero),
D will be scaled by a negative or complex number (or zero).
If RSIGN='F' then the largest (absolute) eigenvalue will be
equal to DMAX.
Not modified.
EI - CHARACTER*1 (ignored)
Not modified.
RSIGN - CHARACTER*1
If MODE is not 0, 6, or -6, and RSIGN='T', then the
elements of D, as computed according to MODE and COND, will
be multiplied by a random complex number from the unit
circle |z| = 1. If RSIGN='F', they will not be. RSIGN may
only have the values 'T' or 'F'.
Not modified.
UPPER - CHARACTER*1
If UPPER='T', then the elements of A above the diagonal
will be set to random numbers out of DIST. If UPPER='F',
they will not. UPPER may only have the values 'T' or 'F'.
Not modified.
SIM - CHARACTER*1
If SIM='T', then A will be operated on by a "similarity
transform", i.e., multiplied on the left by a matrix X and
on the right by X inverse. X = U S V, where U and V are
random unitary matrices and S is a (diagonal) matrix of
singular values specified by DS, MODES, and CONDS. If
SIM='F', then A will not be transformed.
Not modified.
DS - DOUBLE PRECISION array, dimension ( N )
This array is used to specify the singular values of X,
in the same way that D specifies the eigenvalues of A.
If MODE=0, the DS contains the singular values, which
may not be zero.
Modified if MODE is nonzero.
MODES - INTEGER
CONDS - DOUBLE PRECISION
Similar to MODE and COND, but for specifying the diagonal
of S. MODES=-6 and +6 are not allowed (since they would
result in randomly ill-conditioned eigenvalues.)
KL - INTEGER
This specifies the lower bandwidth of the matrix. KL=1
specifies upper Hessenberg form. If KL is at least N-1,
then A will have full lower bandwidth.
Not modified.
KU - INTEGER
This specifies the upper bandwidth of the matrix. KU=1
specifies lower Hessenberg form. If KU is at least N-1,
then A will have full upper bandwidth; if KU and KL
are both at least N-1, then A will be dense. Only one of
KU and KL may be less than N-1.
Not modified.
ANORM - DOUBLE PRECISION
If ANORM is not negative, then A will be scaled by a non-
negative real number to make the maximum-element-norm of A
to be ANORM.
Not modified.
A - COMPLEX*16 array, dimension ( LDA, N )
On exit A is the desired test matrix.
Modified.
LDA - INTEGER
LDA specifies the first dimension of A as declared in the
calling program. LDA must be at least M.
Not modified.
WORK - COMPLEX*16 array, dimension ( 3*N )
Workspace.
Modified.
INFO - INTEGER
Error code. On exit, INFO will be set to one of the
following values:
0 => normal return
-1 => N negative
-2 => DIST illegal string
-5 => MODE not in range -6 to 6
-6 => COND less than 1.0, and MODE neither -6, 0 nor 6
-9 => RSIGN is not 'T' or 'F'
-10 => UPPER is not 'T' or 'F'
-11 => SIM is not 'T' or 'F'
-12 => MODES=0 and DS has a zero singular value.
-13 => MODES is not in the range -5 to 5.
-14 => MODES is nonzero and CONDS is less than 1.
-15 => KL is less than 1.
-16 => KU is less than 1, or KL and KU are both less than
N-1.
-19 => LDA is less than M.
1 => Error return from ZLATM1 (computing D)
2 => Cannot scale to DMAX (max. eigenvalue is 0)
3 => Error return from DLATM1 (computing DS)
4 => Error return from ZLARGE
5 => Zero singular value from DLATM1.
=====================================================================
1) Decode and Test the input parameters.
Initialize flags & seed.
Parameter adjustments */
--iseed;
--d;
--ds;
a_dim1 = *lda;
a_offset = a_dim1 + 1;
a -= a_offset;
--work;
/* Function Body */
*info = 0;
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Decode DIST */
if (lsame_(dist, "U")) {
idist = 1;
} else if (lsame_(dist, "S")) {
idist = 2;
} else if (lsame_(dist, "N")) {
idist = 3;
} else if (lsame_(dist, "D")) {
idist = 4;
} else {
idist = -1;
}
/* Decode RSIGN */
if (lsame_(rsign, "T")) {
irsign = 1;
} else if (lsame_(rsign, "F")) {
irsign = 0;
} else {
irsign = -1;
}
/* Decode UPPER */
if (lsame_(upper, "T")) {
iupper = 1;
} else if (lsame_(upper, "F")) {
iupper = 0;
} else {
iupper = -1;
}
/* Decode SIM */
if (lsame_(sim, "T")) {
isim = 1;
} else if (lsame_(sim, "F")) {
isim = 0;
} else {
isim = -1;
}
/* Check DS, if MODES=0 and ISIM=1 */
bads = FALSE_;
if (*modes == 0 && isim == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (ds[j] == 0.) {
bads = TRUE_;
}
/* L10: */
}
}
/* Set INFO if an error */
if (*n < 0) {
*info = -1;
} else if (idist == -1) {
*info = -2;
} else if (abs(*mode) > 6) {
*info = -5;
} else if (*mode != 0 && abs(*mode) != 6 && *cond < 1.) {
*info = -6;
} else if (irsign == -1) {
*info = -9;
} else if (iupper == -1) {
*info = -10;
} else if (isim == -1) {
*info = -11;
} else if (bads) {
*info = -12;
} else if (isim == 1 && abs(*modes) > 5) {
*info = -13;
} else if (isim == 1 && *modes != 0 && *conds < 1.) {
*info = -14;
} else if (*kl < 1) {
*info = -15;
} else if (*ku < 1 || *ku < *n - 1 && *kl < *n - 1) {
*info = -16;
} else if (*lda < max(1,*n)) {
*info = -19;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZLATME", &i__1);
return 0;
}
/* Initialize random number generator */
for (i = 1; i <= 4; ++i) {
iseed[i] = (i__1 = iseed[i], abs(i__1)) % 4096;
/* L20: */
}
if (iseed[4] % 2 != 1) {
++iseed[4];
}
/* 2) Set up diagonal of A
Compute D according to COND and MODE */
zlatm1_(mode, cond, &irsign, &idist, &iseed[1], &d[1], n, &iinfo);
if (iinfo != 0) {
*info = 1;
return 0;
}
if (*mode != 0 && abs(*mode) != 6) {
/* Scale by DMAX */
temp = z_abs(&d[1]);
i__1 = *n;
for (i = 2; i <= i__1; ++i) {
/* Computing MAX */
d__1 = temp, d__2 = z_abs(&d[i]);
temp = max(d__1,d__2);
/* L30: */
}
if (temp > 0.) {
z__1.r = dmax__->r / temp, z__1.i = dmax__->i / temp;
alpha.r = z__1.r, alpha.i = z__1.i;
} else {
*info = 2;
return 0;
}
zscal_(n, &alpha, &d[1], &c__1);
}
zlaset_("Full", n, n, &c_b1, &c_b1, &a[a_offset], lda);
i__1 = *lda + 1;
zcopy_(n, &d[1], &c__1, &a[a_offset], &i__1);
/* 3) If UPPER='T', set upper triangle of A to random numbers. */
if (iupper != 0) {
i__1 = *n;
for (jc = 2; jc <= i__1; ++jc) {
i__2 = jc - 1;
zlarnv_(&idist, &iseed[1], &i__2, &a[jc * a_dim1 + 1]);
/* L40: */
}
}
/* 4) If SIM='T', apply similarity transformation.
-1
Transform is X A X , where X = U S V, thus
it is U S V A V' (1/S) U' */
if (isim != 0) {
/* Compute S (singular values of the eigenvector matrix)
according to CONDS and MODES */
dlatm1_(modes, conds, &c__0, &c__0, &iseed[1], &ds[1], n, &iinfo);
if (iinfo != 0) {
*info = 3;
return 0;
}
/* Multiply by V and V' */
zlarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo);
if (iinfo != 0) {
*info = 4;
return 0;
}
/* Multiply by S and (1/S) */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
zdscal_(n, &ds[j], &a[j + a_dim1], lda);
if (ds[j] != 0.) {
d__1 = 1. / ds[j];
zdscal_(n, &d__1, &a[j * a_dim1 + 1], &c__1);
} else {
*info = 5;
return 0;
}
/* L50: */
}
/* Multiply by U and U' */
zlarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo);
if (iinfo != 0) {
*info = 4;
return 0;
}
}
/* 5) Reduce the bandwidth. */
if (*kl < *n - 1) {
/* Reduce bandwidth -- kill column */
i__1 = *n - 1;
for (jcr = *kl + 1; jcr <= i__1; ++jcr) {
ic = jcr - *kl;
irows = *n + 1 - jcr;
icols = *n + *kl - jcr;
zcopy_(&irows, &a[jcr + ic * a_dim1], &c__1, &work[1], &c__1);
xnorms.r = work[1].r, xnorms.i = work[1].i;
zlarfg_(&irows, &xnorms, &work[2], &c__1, &tau);
d_cnjg(&z__1, &tau);
tau.r = z__1.r, tau.i = z__1.i;
work[1].r = 1., work[1].i = 0.;
zlarnd_(&z__1, &c__5, &iseed[1]);
alpha.r = z__1.r, alpha.i = z__1.i;
zgemv_("C", &irows, &icols, &c_b2, &a[jcr + (ic + 1) * a_dim1],
lda, &work[1], &c__1, &c_b1, &work[irows + 1], &c__1);
z__1.r = -tau.r, z__1.i = -tau.i;
zgerc_(&irows, &icols, &z__1, &work[1], &c__1, &work[irows + 1], &
c__1, &a[jcr + (ic + 1) * a_dim1], lda);
zgemv_("N", n, &irows, &c_b2, &a[jcr * a_dim1 + 1], lda, &work[1],
&c__1, &c_b1, &work[irows + 1], &c__1);
d_cnjg(&z__2, &tau);
z__1.r = -z__2.r, z__1.i = -z__2.i;
zgerc_(n, &irows, &z__1, &work[irows + 1], &c__1, &work[1], &c__1,
&a[jcr * a_dim1 + 1], lda);
i__2 = jcr + ic * a_dim1;
a[i__2].r = xnorms.r, a[i__2].i = xnorms.i;
i__2 = irows - 1;
zlaset_("Full", &i__2, &c__1, &c_b1, &c_b1, &a[jcr + 1 + ic *
a_dim1], lda);
i__2 = icols + 1;
zscal_(&i__2, &alpha, &a[jcr + ic * a_dim1], lda);
d_cnjg(&z__1, &alpha);
zscal_(n, &z__1, &a[jcr * a_dim1 + 1], &c__1);
/* L60: */
}
} else if (*ku < *n - 1) {
/* Reduce upper bandwidth -- kill a row at a time. */
i__1 = *n - 1;
for (jcr = *ku + 1; jcr <= i__1; ++jcr) {
ir = jcr - *ku;
irows = *n + *ku - jcr;
icols = *n + 1 - jcr;
zcopy_(&icols, &a[ir + jcr * a_dim1], lda, &work[1], &c__1);
xnorms.r = work[1].r, xnorms.i = work[1].i;
zlarfg_(&icols, &xnorms, &work[2], &c__1, &tau);
d_cnjg(&z__1, &tau);
tau.r = z__1.r, tau.i = z__1.i;
work[1].r = 1., work[1].i = 0.;
i__2 = icols - 1;
zlacgv_(&i__2, &work[2], &c__1);
zlarnd_(&z__1, &c__5, &iseed[1]);
alpha.r = z__1.r, alpha.i = z__1.i;
zgemv_("N", &irows, &icols, &c_b2, &a[ir + 1 + jcr * a_dim1], lda,
&work[1], &c__1, &c_b1, &work[icols + 1], &c__1);
z__1.r = -tau.r, z__1.i = -tau.i;
zgerc_(&irows, &icols, &z__1, &work[icols + 1], &c__1, &work[1], &
c__1, &a[ir + 1 + jcr * a_dim1], lda);
zgemv_("C", &icols, n, &c_b2, &a[jcr + a_dim1], lda, &work[1], &
c__1, &c_b1, &work[icols + 1], &c__1);
d_cnjg(&z__2, &tau);
z__1.r = -z__2.r, z__1.i = -z__2.i;
zgerc_(&icols, n, &z__1, &work[1], &c__1, &work[icols + 1], &c__1,
&a[jcr + a_dim1], lda);
i__2 = ir + jcr * a_dim1;
a[i__2].r = xnorms.r, a[i__2].i = xnorms.i;
i__2 = icols - 1;
zlaset_("Full", &c__1, &i__2, &c_b1, &c_b1, &a[ir + (jcr + 1) *
a_dim1], lda);
i__2 = irows + 1;
zscal_(&i__2, &alpha, &a[ir + jcr * a_dim1], &c__1);
d_cnjg(&z__1, &alpha);
zscal_(n, &z__1, &a[jcr + a_dim1], lda);
/* L70: */
}
}
/* Scale the matrix to have norm ANORM */
if (*anorm >= 0.) {
temp = zlange_("M", n, n, &a[a_offset], lda, tempa);
if (temp > 0.) {
ralpha = *anorm / temp;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
zdscal_(n, &ralpha, &a[j * a_dim1 + 1], &c__1);
/* L80: */
}
}
}
return 0;
/* End of ZLATME */
} /* zlatme_ */
/* Subroutine */ int zlattr_(integer *imat, char *uplo, char *trans, char *
diag, integer *iseed, integer *n, doublecomplex *a, integer *lda,
doublecomplex *b, doublecomplex *work, doublereal *rwork, integer *
info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
double pow_dd(doublereal *, doublereal *), sqrt(doublereal);
void d_cnjg(doublecomplex *, doublecomplex *);
double z_abs(doublecomplex *);
/* Local variables */
doublereal c__;
integer i__, j;
doublecomplex s;
doublereal x, y, z__;
doublecomplex ra, rb;
integer kl, ku, iy;
doublereal ulp, sfac;
integer mode;
char path[3], dist[1];
doublereal unfl, rexp;
char type__[1];
doublereal texp;
extern /* Subroutine */ int zrot_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublecomplex *);
doublecomplex star1, plus1, plus2;
doublereal bscal;
extern logical lsame_(char *, char *);
doublereal tscal, anorm, bnorm, tleft;
logical upper;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zrotg_(doublecomplex *,
doublecomplex *, doublereal *, doublecomplex *), zswap_(integer *,
doublecomplex *, integer *, doublecomplex *, integer *), zlatb4_(
char *, integer *, integer *, integer *, char *, integer *,
integer *, doublereal *, integer *, doublereal *, char *), dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *), dlarnd_(integer *, integer *);
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *);
doublereal bignum, cndnum;
extern /* Subroutine */ int dlarnv_(integer *, integer *, integer *,
doublereal *);
extern integer izamax_(integer *, doublecomplex *, integer *);
extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *,
integer *);
integer jcount;
extern /* Subroutine */ int zlatms_(integer *, integer *, char *, integer
*, char *, doublereal *, integer *, doublereal *, doublereal *,
integer *, integer *, char *, doublecomplex *, integer *,
doublecomplex *, integer *);
doublereal smlnum;
extern /* Subroutine */ int zlarnv_(integer *, integer *, integer *,
doublecomplex *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLATTR generates a triangular test matrix in 2-dimensional storage. */
/* IMAT and UPLO uniquely specify the properties of the test matrix, */
/* which is returned in the array A. */
/* Arguments */
/* ========= */
/* IMAT (input) INTEGER */
/* An integer key describing which matrix to generate for this */
/* path. */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the matrix A will be upper or lower */
/* triangular. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* TRANS (input) CHARACTER*1 */
/* Specifies whether the matrix or its transpose will be used. */
/* = 'N': No transpose */
/* = 'T': Transpose */
/* = 'C': Conjugate transpose */
/* DIAG (output) CHARACTER*1 */
/* Specifies whether or not the matrix A is unit triangular. */
/* = 'N': Non-unit triangular */
/* = 'U': Unit triangular */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* The seed vector for the random number generator (used in */
/* ZLATMS). Modified on exit. */
/* N (input) INTEGER */
/* The order of the matrix to be generated. */
/* A (output) COMPLEX*16 array, dimension (LDA,N) */
/* The triangular matrix A. If UPLO = 'U', the leading N x N */
/* upper triangular part of the array A contains the upper */
/* triangular matrix, and the strictly lower triangular part of */
/* A is not referenced. If UPLO = 'L', the leading N x N lower */
/* triangular part of the array A contains the lower triangular */
/* matrix and the strictly upper triangular part of A is not */
/* referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (output) COMPLEX*16 array, dimension (N) */
/* The right hand side vector, if IMAT > 10. */
/* WORK (workspace) COMPLEX*16 array, dimension (2*N) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--iseed;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--b;
--work;
--rwork;
/* Function Body */
s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "TR", (ftnlen)2, (ftnlen)2);
unfl = dlamch_("Safe minimum");
ulp = dlamch_("Epsilon") * dlamch_("Base");
smlnum = unfl;
bignum = (1. - ulp) / smlnum;
dlabad_(&smlnum, &bignum);
if (*imat >= 7 && *imat <= 10 || *imat == 18) {
*(unsigned char *)diag = 'U';
} else {
*(unsigned char *)diag = 'N';
}
*info = 0;
/* Quick return if N.LE.0. */
if (*n <= 0) {
return 0;
}
/* Call ZLATB4 to set parameters for CLATMS. */
upper = lsame_(uplo, "U");
if (upper) {
zlatb4_(path, imat, n, n, type__, &kl, &ku, &anorm, &mode, &cndnum,
dist);
} else {
i__1 = -(*imat);
zlatb4_(path, &i__1, n, n, type__, &kl, &ku, &anorm, &mode, &cndnum,
dist);
}
/* IMAT <= 6: Non-unit triangular matrix */
if (*imat <= 6) {
zlatms_(n, n, dist, &iseed[1], type__, &rwork[1], &mode, &cndnum, &
anorm, &kl, &ku, "No packing", &a[a_offset], lda, &work[1],
info);
/* IMAT > 6: Unit triangular matrix */
/* The diagonal is deliberately set to something other than 1. */
/* IMAT = 7: Matrix is the identity */
} else if (*imat == 7) {
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L10: */
}
i__2 = j + j * a_dim1;
a[i__2].r = (doublereal) j, a[i__2].i = 0.;
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j + j * a_dim1;
a[i__2].r = (doublereal) j, a[i__2].i = 0.;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L30: */
}
/* L40: */
}
}
/* IMAT > 7: Non-trivial unit triangular matrix */
/* Generate a unit triangular matrix T with condition CNDNUM by */
/* forming a triangular matrix with known singular values and */
/* filling in the zero entries with Givens rotations. */
} else if (*imat <= 10) {
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L50: */
}
i__2 = j + j * a_dim1;
a[i__2].r = (doublereal) j, a[i__2].i = 0.;
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j + j * a_dim1;
a[i__2].r = (doublereal) j, a[i__2].i = 0.;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L70: */
}
/* L80: */
}
}
/* Since the trace of a unit triangular matrix is 1, the product */
/* of its singular values must be 1. Let s = sqrt(CNDNUM), */
/* x = sqrt(s) - 1/sqrt(s), y = sqrt(2/(n-2))*x, and z = x**2. */
/* The following triangular matrix has singular values s, 1, 1, */
/* ..., 1, 1/s: */
/* 1 y y y ... y y z */
/* 1 0 0 ... 0 0 y */
/* 1 0 ... 0 0 y */
/* . ... . . . */
/* . . . . */
/* 1 0 y */
/* 1 y */
/* 1 */
/* To fill in the zeros, we first multiply by a matrix with small */
/* condition number of the form */
/* 1 0 0 0 0 ... */
/* 1 + * 0 0 ... */
/* 1 + 0 0 0 */
/* 1 + * 0 0 */
/* 1 + 0 0 */
/* ... */
/* 1 + 0 */
/* 1 0 */
/* 1 */
/* Each element marked with a '*' is formed by taking the product */
/* of the adjacent elements marked with '+'. The '*'s can be */
/* chosen freely, and the '+'s are chosen so that the inverse of */
/* T will have elements of the same magnitude as T. If the *'s in */
/* both T and inv(T) have small magnitude, T is well conditioned. */
/* The two offdiagonals of T are stored in WORK. */
/* The product of these two matrices has the form */
/* 1 y y y y y . y y z */
/* 1 + * 0 0 . 0 0 y */
/* 1 + 0 0 . 0 0 y */
/* 1 + * . . . . */
/* 1 + . . . . */
/* . . . . . */
/* . . . . */
/* 1 + y */
/* 1 y */
/* 1 */
/* Now we multiply by Givens rotations, using the fact that */
/* [ c s ] [ 1 w ] [ -c -s ] = [ 1 -w ] */
/* [ -s c ] [ 0 1 ] [ s -c ] [ 0 1 ] */
/* and */
/* [ -c -s ] [ 1 0 ] [ c s ] = [ 1 0 ] */
/* [ s -c ] [ w 1 ] [ -s c ] [ -w 1 ] */
/* where c = w / sqrt(w**2+4) and s = 2 / sqrt(w**2+4). */
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r * .25, z__1.i = z__2.i * .25;
star1.r = z__1.r, star1.i = z__1.i;
sfac = .5;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = sfac * z__2.r, z__1.i = sfac * z__2.i;
plus1.r = z__1.r, plus1.i = z__1.i;
i__1 = *n;
for (j = 1; j <= i__1; j += 2) {
z_div(&z__1, &star1, &plus1);
plus2.r = z__1.r, plus2.i = z__1.i;
i__2 = j;
work[i__2].r = plus1.r, work[i__2].i = plus1.i;
i__2 = *n + j;
work[i__2].r = star1.r, work[i__2].i = star1.i;
if (j + 1 <= *n) {
i__2 = j + 1;
work[i__2].r = plus2.r, work[i__2].i = plus2.i;
i__2 = *n + j + 1;
work[i__2].r = 0., work[i__2].i = 0.;
z_div(&z__1, &star1, &plus2);
plus1.r = z__1.r, plus1.i = z__1.i;
rexp = dlarnd_(&c__2, &iseed[1]);
if (rexp < 0.) {
d__2 = 1. - rexp;
d__1 = -pow_dd(&sfac, &d__2);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = d__1 * z__2.r, z__1.i = d__1 * z__2.i;
star1.r = z__1.r, star1.i = z__1.i;
} else {
d__2 = rexp + 1.;
d__1 = pow_dd(&sfac, &d__2);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = d__1 * z__2.r, z__1.i = d__1 * z__2.i;
star1.r = z__1.r, star1.i = z__1.i;
}
}
/* L90: */
}
x = sqrt(cndnum) - 1 / sqrt(cndnum);
if (*n > 2) {
y = sqrt(2. / (*n - 2)) * x;
} else {
y = 0.;
}
z__ = x * x;
if (upper) {
if (*n > 3) {
i__1 = *n - 3;
i__2 = *lda + 1;
zcopy_(&i__1, &work[1], &c__1, &a[a_dim1 * 3 + 2], &i__2);
if (*n > 4) {
i__1 = *n - 4;
i__2 = *lda + 1;
zcopy_(&i__1, &work[*n + 1], &c__1, &a[(a_dim1 << 2) + 2],
&i__2);
}
}
i__1 = *n - 1;
for (j = 2; j <= i__1; ++j) {
i__2 = j * a_dim1 + 1;
a[i__2].r = y, a[i__2].i = 0.;
i__2 = j + *n * a_dim1;
a[i__2].r = y, a[i__2].i = 0.;
/* L100: */
}
i__1 = *n * a_dim1 + 1;
a[i__1].r = z__, a[i__1].i = 0.;
} else {
if (*n > 3) {
i__1 = *n - 3;
i__2 = *lda + 1;
zcopy_(&i__1, &work[1], &c__1, &a[(a_dim1 << 1) + 3], &i__2);
if (*n > 4) {
i__1 = *n - 4;
i__2 = *lda + 1;
zcopy_(&i__1, &work[*n + 1], &c__1, &a[(a_dim1 << 1) + 4],
&i__2);
}
}
i__1 = *n - 1;
for (j = 2; j <= i__1; ++j) {
i__2 = j + a_dim1;
a[i__2].r = y, a[i__2].i = 0.;
i__2 = *n + j * a_dim1;
a[i__2].r = y, a[i__2].i = 0.;
/* L110: */
}
i__1 = *n + a_dim1;
a[i__1].r = z__, a[i__1].i = 0.;
}
/* Fill in the zeros using Givens rotations. */
if (upper) {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = j + (j + 1) * a_dim1;
ra.r = a[i__2].r, ra.i = a[i__2].i;
rb.r = 2., rb.i = 0.;
zrotg_(&ra, &rb, &c__, &s);
/* Multiply by [ c s; -conjg(s) c] on the left. */
if (*n > j + 1) {
i__2 = *n - j - 1;
zrot_(&i__2, &a[j + (j + 2) * a_dim1], lda, &a[j + 1 + (j
+ 2) * a_dim1], lda, &c__, &s);
}
/* Multiply by [-c -s; conjg(s) -c] on the right. */
if (j > 1) {
i__2 = j - 1;
d__1 = -c__;
z__1.r = -s.r, z__1.i = -s.i;
zrot_(&i__2, &a[(j + 1) * a_dim1 + 1], &c__1, &a[j *
a_dim1 + 1], &c__1, &d__1, &z__1);
}
/* Negate A(J,J+1). */
i__2 = j + (j + 1) * a_dim1;
i__3 = j + (j + 1) * a_dim1;
z__1.r = -a[i__3].r, z__1.i = -a[i__3].i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L120: */
}
} else {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = j + 1 + j * a_dim1;
ra.r = a[i__2].r, ra.i = a[i__2].i;
rb.r = 2., rb.i = 0.;
zrotg_(&ra, &rb, &c__, &s);
d_cnjg(&z__1, &s);
s.r = z__1.r, s.i = z__1.i;
/* Multiply by [ c -s; conjg(s) c] on the right. */
if (*n > j + 1) {
i__2 = *n - j - 1;
z__1.r = -s.r, z__1.i = -s.i;
zrot_(&i__2, &a[j + 2 + (j + 1) * a_dim1], &c__1, &a[j +
2 + j * a_dim1], &c__1, &c__, &z__1);
}
/* Multiply by [-c s; -conjg(s) -c] on the left. */
if (j > 1) {
i__2 = j - 1;
d__1 = -c__;
zrot_(&i__2, &a[j + a_dim1], lda, &a[j + 1 + a_dim1], lda,
&d__1, &s);
}
/* Negate A(J+1,J). */
i__2 = j + 1 + j * a_dim1;
i__3 = j + 1 + j * a_dim1;
z__1.r = -a[i__3].r, z__1.i = -a[i__3].i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L130: */
}
}
/* IMAT > 10: Pathological test cases. These triangular matrices */
/* are badly scaled or badly conditioned, so when used in solving a */
/* triangular system they may cause overflow in the solution vector. */
} else if (*imat == 11) {
/* Type 11: Generate a triangular matrix with elements between */
/* -1 and 1. Give the diagonal norm 2 to make it well-conditioned. */
/* Make the right hand side large so that it requires scaling. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
zlarnv_(&c__4, &iseed[1], &i__2, &a[j * a_dim1 + 1]);
i__2 = j + j * a_dim1;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r * 2., z__1.i = z__2.i * 2.;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L140: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (j < *n) {
i__2 = *n - j;
zlarnv_(&c__4, &iseed[1], &i__2, &a[j + 1 + j * a_dim1]);
}
i__2 = j + j * a_dim1;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r * 2., z__1.i = z__2.i * 2.;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L150: */
}
}
/* Set the right hand side so that the largest value is BIGNUM. */
zlarnv_(&c__2, &iseed[1], n, &b[1]);
iy = izamax_(n, &b[1], &c__1);
bnorm = z_abs(&b[iy]);
bscal = bignum / max(1.,bnorm);
zdscal_(n, &bscal, &b[1], &c__1);
} else if (*imat == 12) {
/* Type 12: Make the first diagonal element in the solve small to */
/* cause immediate overflow when dividing by T(j,j). */
/* In type 12, the offdiagonal elements are small (CNORM(j) < 1). */
zlarnv_(&c__2, &iseed[1], n, &b[1]);
/* Computing MAX */
d__1 = 1., d__2 = (doublereal) (*n - 1);
tscal = 1. / max(d__1,d__2);
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
zlarnv_(&c__4, &iseed[1], &i__2, &a[j * a_dim1 + 1]);
i__2 = j - 1;
zdscal_(&i__2, &tscal, &a[j * a_dim1 + 1], &c__1);
i__2 = j + j * a_dim1;
zlarnd_(&z__1, &c__5, &iseed[1]);
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L160: */
}
i__1 = *n + *n * a_dim1;
i__2 = *n + *n * a_dim1;
z__1.r = smlnum * a[i__2].r, z__1.i = smlnum * a[i__2].i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (j < *n) {
i__2 = *n - j;
zlarnv_(&c__4, &iseed[1], &i__2, &a[j + 1 + j * a_dim1]);
i__2 = *n - j;
zdscal_(&i__2, &tscal, &a[j + 1 + j * a_dim1], &c__1);
}
i__2 = j + j * a_dim1;
zlarnd_(&z__1, &c__5, &iseed[1]);
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L170: */
}
i__1 = a_dim1 + 1;
i__2 = a_dim1 + 1;
z__1.r = smlnum * a[i__2].r, z__1.i = smlnum * a[i__2].i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
}
} else if (*imat == 13) {
/* Type 13: Make the first diagonal element in the solve small to */
/* cause immediate overflow when dividing by T(j,j). */
/* In type 13, the offdiagonal elements are O(1) (CNORM(j) > 1). */
zlarnv_(&c__2, &iseed[1], n, &b[1]);
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
zlarnv_(&c__4, &iseed[1], &i__2, &a[j * a_dim1 + 1]);
i__2 = j + j * a_dim1;
zlarnd_(&z__1, &c__5, &iseed[1]);
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L180: */
}
i__1 = *n + *n * a_dim1;
i__2 = *n + *n * a_dim1;
z__1.r = smlnum * a[i__2].r, z__1.i = smlnum * a[i__2].i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (j < *n) {
i__2 = *n - j;
zlarnv_(&c__4, &iseed[1], &i__2, &a[j + 1 + j * a_dim1]);
}
i__2 = j + j * a_dim1;
zlarnd_(&z__1, &c__5, &iseed[1]);
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L190: */
}
i__1 = a_dim1 + 1;
i__2 = a_dim1 + 1;
z__1.r = smlnum * a[i__2].r, z__1.i = smlnum * a[i__2].i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
}
} else if (*imat == 14) {
/* Type 14: T is diagonal with small numbers on the diagonal to */
/* make the growth factor underflow, but a small right hand side */
/* chosen so that the solution does not overflow. */
if (upper) {
jcount = 1;
for (j = *n; j >= 1; --j) {
i__1 = j - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * a_dim1;
a[i__2].r = 0., a[i__2].i = 0.;
/* L200: */
}
if (jcount <= 2) {
i__1 = j + j * a_dim1;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = smlnum * z__2.r, z__1.i = smlnum * z__2.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
} else {
i__1 = j + j * a_dim1;
zlarnd_(&z__1, &c__5, &iseed[1]);
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
}
++jcount;
if (jcount > 4) {
jcount = 1;
}
/* L210: */
}
} else {
jcount = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L220: */
}
if (jcount <= 2) {
i__2 = j + j * a_dim1;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = smlnum * z__2.r, z__1.i = smlnum * z__2.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
} else {
i__2 = j + j * a_dim1;
zlarnd_(&z__1, &c__5, &iseed[1]);
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
}
++jcount;
if (jcount > 4) {
jcount = 1;
}
/* L230: */
}
}
/* Set the right hand side alternately zero and small. */
if (upper) {
b[1].r = 0., b[1].i = 0.;
for (i__ = *n; i__ >= 2; i__ += -2) {
i__1 = i__;
b[i__1].r = 0., b[i__1].i = 0.;
i__1 = i__ - 1;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = smlnum * z__2.r, z__1.i = smlnum * z__2.i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
/* L240: */
}
} else {
i__1 = *n;
b[i__1].r = 0., b[i__1].i = 0.;
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; i__ += 2) {
i__2 = i__;
b[i__2].r = 0., b[i__2].i = 0.;
i__2 = i__ + 1;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = smlnum * z__2.r, z__1.i = smlnum * z__2.i;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L250: */
}
}
} else if (*imat == 15) {
/* Type 15: Make the diagonal elements small to cause gradual */
/* overflow when dividing by T(j,j). To control the amount of */
/* scaling needed, the matrix is bidiagonal. */
/* Computing MAX */
d__1 = 1., d__2 = (doublereal) (*n - 1);
texp = 1. / max(d__1,d__2);
tscal = pow_dd(&smlnum, &texp);
zlarnv_(&c__4, &iseed[1], n, &b[1]);
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 2;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L260: */
}
if (j > 1) {
i__2 = j - 1 + j * a_dim1;
a[i__2].r = -1., a[i__2].i = -1.;
}
i__2 = j + j * a_dim1;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = tscal * z__2.r, z__1.i = tscal * z__2.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L270: */
}
i__1 = *n;
b[i__1].r = 1., b[i__1].i = 1.;
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j + 2; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L280: */
}
if (j < *n) {
i__2 = j + 1 + j * a_dim1;
a[i__2].r = -1., a[i__2].i = -1.;
}
i__2 = j + j * a_dim1;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = tscal * z__2.r, z__1.i = tscal * z__2.i;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
/* L290: */
}
b[1].r = 1., b[1].i = 1.;
}
} else if (*imat == 16) {
/* Type 16: One zero diagonal element. */
iy = *n / 2 + 1;
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
zlarnv_(&c__4, &iseed[1], &i__2, &a[j * a_dim1 + 1]);
if (j != iy) {
i__2 = j + j * a_dim1;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r * 2., z__1.i = z__2.i * 2.;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
} else {
i__2 = j + j * a_dim1;
a[i__2].r = 0., a[i__2].i = 0.;
}
/* L300: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (j < *n) {
i__2 = *n - j;
zlarnv_(&c__4, &iseed[1], &i__2, &a[j + 1 + j * a_dim1]);
}
if (j != iy) {
i__2 = j + j * a_dim1;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r * 2., z__1.i = z__2.i * 2.;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
} else {
i__2 = j + j * a_dim1;
a[i__2].r = 0., a[i__2].i = 0.;
}
/* L310: */
}
}
zlarnv_(&c__2, &iseed[1], n, &b[1]);
zdscal_(n, &c_b92, &b[1], &c__1);
} else if (*imat == 17) {
/* Type 17: Make the offdiagonal elements large to cause overflow */
/* when adding a column of T. In the non-transposed case, the */
/* matrix is constructed to cause overflow when adding a column in */
/* every other step. */
tscal = unfl / ulp;
tscal = (1. - ulp) / tscal;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L320: */
}
/* L330: */
}
texp = 1.;
if (upper) {
for (j = *n; j >= 2; j += -2) {
i__1 = j * a_dim1 + 1;
d__1 = -tscal / (doublereal) (*n + 1);
a[i__1].r = d__1, a[i__1].i = 0.;
i__1 = j + j * a_dim1;
a[i__1].r = 1., a[i__1].i = 0.;
i__1 = j;
d__1 = texp * (1. - ulp);
b[i__1].r = d__1, b[i__1].i = 0.;
i__1 = (j - 1) * a_dim1 + 1;
d__1 = -(tscal / (doublereal) (*n + 1)) / (doublereal) (*n +
2);
a[i__1].r = d__1, a[i__1].i = 0.;
i__1 = j - 1 + (j - 1) * a_dim1;
a[i__1].r = 1., a[i__1].i = 0.;
i__1 = j - 1;
d__1 = texp * (doublereal) (*n * *n + *n - 1);
b[i__1].r = d__1, b[i__1].i = 0.;
texp *= 2.;
/* L340: */
}
d__1 = (doublereal) (*n + 1) / (doublereal) (*n + 2) * tscal;
b[1].r = d__1, b[1].i = 0.;
} else {
i__1 = *n - 1;
for (j = 1; j <= i__1; j += 2) {
i__2 = *n + j * a_dim1;
d__1 = -tscal / (doublereal) (*n + 1);
a[i__2].r = d__1, a[i__2].i = 0.;
i__2 = j + j * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
i__2 = j;
d__1 = texp * (1. - ulp);
b[i__2].r = d__1, b[i__2].i = 0.;
i__2 = *n + (j + 1) * a_dim1;
d__1 = -(tscal / (doublereal) (*n + 1)) / (doublereal) (*n +
2);
a[i__2].r = d__1, a[i__2].i = 0.;
i__2 = j + 1 + (j + 1) * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
i__2 = j + 1;
d__1 = texp * (doublereal) (*n * *n + *n - 1);
b[i__2].r = d__1, b[i__2].i = 0.;
texp *= 2.;
/* L350: */
}
i__1 = *n;
d__1 = (doublereal) (*n + 1) / (doublereal) (*n + 2) * tscal;
b[i__1].r = d__1, b[i__1].i = 0.;
}
} else if (*imat == 18) {
/* Type 18: Generate a unit triangular matrix with elements */
/* between -1 and 1, and make the right hand side large so that it */
/* requires scaling. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
zlarnv_(&c__4, &iseed[1], &i__2, &a[j * a_dim1 + 1]);
i__2 = j + j * a_dim1;
a[i__2].r = 0., a[i__2].i = 0.;
/* L360: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (j < *n) {
i__2 = *n - j;
zlarnv_(&c__4, &iseed[1], &i__2, &a[j + 1 + j * a_dim1]);
}
i__2 = j + j * a_dim1;
a[i__2].r = 0., a[i__2].i = 0.;
/* L370: */
}
}
/* Set the right hand side so that the largest value is BIGNUM. */
zlarnv_(&c__2, &iseed[1], n, &b[1]);
iy = izamax_(n, &b[1], &c__1);
bnorm = z_abs(&b[iy]);
bscal = bignum / max(1.,bnorm);
zdscal_(n, &bscal, &b[1], &c__1);
} else if (*imat == 19) {
/* Type 19: Generate a triangular matrix with elements between */
/* BIGNUM/(n-1) and BIGNUM so that at least one of the column */
/* norms will exceed BIGNUM. */
/* 1/3/91: ZLATRS no longer can handle this case */
/* Computing MAX */
d__1 = 1., d__2 = (doublereal) (*n - 1);
tleft = bignum / max(d__1,d__2);
/* Computing MAX */
d__1 = 1., d__2 = (doublereal) (*n);
tscal = bignum * ((doublereal) (*n - 1) / max(d__1,d__2));
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
zlarnv_(&c__5, &iseed[1], &j, &a[j * a_dim1 + 1]);
dlarnv_(&c__1, &iseed[1], &j, &rwork[1]);
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
d__1 = tleft + rwork[i__] * tscal;
z__1.r = d__1 * a[i__4].r, z__1.i = d__1 * a[i__4].i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L380: */
}
/* L390: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n - j + 1;
zlarnv_(&c__5, &iseed[1], &i__2, &a[j + j * a_dim1]);
i__2 = *n - j + 1;
dlarnv_(&c__1, &iseed[1], &i__2, &rwork[1]);
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
d__1 = tleft + rwork[i__ - j + 1] * tscal;
z__1.r = d__1 * a[i__4].r, z__1.i = d__1 * a[i__4].i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L400: */
}
/* L410: */
}
}
zlarnv_(&c__2, &iseed[1], n, &b[1]);
zdscal_(n, &c_b92, &b[1], &c__1);
}
/* Flip the matrix if the transpose will be used. */
if (! lsame_(trans, "N")) {
if (upper) {
i__1 = *n / 2;
for (j = 1; j <= i__1; ++j) {
i__2 = *n - (j << 1) + 1;
zswap_(&i__2, &a[j + j * a_dim1], lda, &a[j + 1 + (*n - j + 1)
* a_dim1], &c_n1);
/* L420: */
}
} else {
i__1 = *n / 2;
for (j = 1; j <= i__1; ++j) {
i__2 = *n - (j << 1) + 1;
i__3 = -(*lda);
zswap_(&i__2, &a[j + j * a_dim1], &c__1, &a[*n - j + 1 + (j +
1) * a_dim1], &i__3);
/* L430: */
}
}
}
return 0;
/* End of ZLATTR */
} /* zlattr_ */
/* Subroutine */ int zdrvgg_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, doublereal *thresh, doublereal *
thrshn, integer *nounit, doublecomplex *a, integer *lda,
doublecomplex *b, doublecomplex *s, doublecomplex *t, doublecomplex *
s2, doublecomplex *t2, doublecomplex *q, integer *ldq, doublecomplex *
z__, doublecomplex *alpha1, doublecomplex *beta1, doublecomplex *
alpha2, doublecomplex *beta2, doublecomplex *vl, doublecomplex *vr,
doublecomplex *work, integer *lwork, doublereal *rwork, doublereal *
result, integer *info)
{
/* Initialized data */
static integer kclass[26] = { 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,2,3 };
static integer kbmagn[26] = { 1,1,1,1,1,1,1,1,3,2,3,2,2,3,1,1,1,1,1,1,1,3,
2,3,2,1 };
static integer ktrian[26] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,
1,1,1,1 };
static logical lasign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
TRUE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,TRUE_,TRUE_,FALSE_ };
static logical lbsign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_ };
static integer kz1[6] = { 0,1,2,1,3,3 };
static integer kz2[6] = { 0,0,1,2,1,1 };
static integer kadd[6] = { 0,0,0,0,3,2 };
static integer katype[26] = { 0,1,0,1,2,3,4,1,4,4,1,1,4,4,4,2,4,5,8,7,9,4,
4,4,4,0 };
static integer kbtype[26] = { 0,0,1,1,2,-3,1,4,1,1,4,4,1,1,-4,2,-4,8,8,8,
8,8,8,8,8,0 };
static integer kazero[26] = { 1,1,1,1,1,1,2,1,2,2,1,1,2,2,3,1,3,5,5,5,5,3,
3,3,3,1 };
static integer kbzero[26] = { 1,1,1,1,1,1,1,2,1,1,2,2,1,1,4,1,4,6,6,6,6,4,
4,4,4,1 };
static integer kamagn[26] = { 1,1,1,1,1,1,1,1,2,3,2,3,2,3,1,1,1,1,1,1,1,2,
3,3,2,1 };
/* Format strings */
static char fmt_9999[] = "(\002 ZDRVGG: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
"(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9998[] = "(\002 ZDRVGG: \002,a,\002 Eigenvectors from"
" \002,a,\002 incorrectly \002,\002normalized.\002,/\002 Bits of "
"error=\002,0p,g10.3,\002,\002,9x,\002N=\002,i6,\002, JTYPE=\002,"
"i6,\002, ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9997[] = "(/1x,a3,\002 -- Complex Generalized eigenvalue"
" problem driver\002)";
static char fmt_9996[] = "(\002 Matrix types (see ZDRVGG for details):"
" \002)";
static char fmt_9995[] = "(\002 Special Matrices:\002,23x,\002(J'=transp"
"osed Jordan block)\002,/\002 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I"
") 5=(J',J') \002,\0026=(diag(J',I), diag(I,J'))\002,/\002 Diag"
"onal Matrices: ( \002,\002D=diag(0,1,2,...) )\002,/\002 7=(D,"
"I) 9=(large*D, small*I\002,\002) 11=(large*I, small*D) 13=(l"
"arge*D, large*I)\002,/\002 8=(I,D) 10=(small*D, large*I) 12="
"(small*I, large*D) \002,\002 14=(small*D, small*I)\002,/\002 15"
"=(D, reversed D)\002)";
static char fmt_9994[] = "(\002 Matrices Rotated by Random \002,a,\002 M"
"atrices U, V:\002,/\002 16=Transposed Jordan Blocks "
" 19=geometric \002,\002alpha, beta=0,1\002,/\002 17=arithm. alp"
"ha&beta \002,\002 20=arithmetic alpha, beta=0,"
"1\002,/\002 18=clustered \002,\002alpha, beta=0,1 21"
"=random alpha, beta=0,1\002,/\002 Large & Small Matrices:\002,"
"/\002 22=(large, small) \002,\00223=(small,large) 24=(smal"
"l,small) 25=(large,large)\002,/\002 26=random O(1) matrices"
".\002)";
static char fmt_9993[] = "(/\002 Tests performed: (S is Schur, T is tri"
"angular, \002,\002Q and Z are \002,a,\002,\002,/20x,\002l and r "
"are the appropriate left and right\002,/19x,\002eigenvectors, re"
"sp., a is alpha, b is beta, and\002,/19x,a,\002 means \002,a,"
"\002.)\002,/\002 1 = | A - Q S Z\002,a,\002 | / ( |A| n ulp ) "
" 2 = | B - Q T Z\002,a,\002 | / ( |B| n ulp )\002,/\002 3 = | "
"I - QQ\002,a,\002 | / ( n ulp ) 4 = | I - ZZ\002,a"
",\002 | / ( n ulp )\002,/\002 5 = difference between (alpha,beta"
") and diagonals of\002,\002 (S,T)\002,/\002 6 = max | ( b A - a "
"B )\002,a,\002 l | / const. 7 = max | ( b A - a B ) r | / cons"
"t.\002,/1x)";
static char fmt_9992[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i3,\002 is\002"
",0p,f8.2)";
static char fmt_9991[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i3,\002 is\002"
",1p,d10.3)";
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, s_dim1,
s_offset, s2_dim1, s2_offset, t_dim1, t_offset, t2_dim1,
t2_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, z_dim1,
z_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9,
i__10, i__11;
doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10,
d__11, d__12, d__13, d__14, d__15, d__16;
doublecomplex z__1, z__2, z__3, z__4;
/* Builtin functions */
double d_sign(doublereal *, doublereal *), z_abs(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
double d_imag(doublecomplex *);
/* Local variables */
integer j, n, i1, n1, jc, nb, in, jr, ns, nbz;
doublereal ulp;
integer iadd, nmax;
doublereal temp1, temp2;
logical badnn;
doublereal dumma[4];
integer iinfo;
doublereal rmagn[4];
doublecomplex ctemp;
extern /* Subroutine */ int zgegs_(char *, char *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *), zget51_(integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublereal *, doublereal *), zget52_(logical *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
doublecomplex *, doublereal *, doublereal *);
integer nmats, jsize;
extern /* Subroutine */ int zgegv_(char *, char *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *);
integer nerrs, jtype, ntest;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), zlatm4_(
integer *, integer *, integer *, integer *, logical *, doublereal
*, doublereal *, doublereal *, integer *, integer *,
doublecomplex *, integer *);
extern doublereal dlamch_(char *);
extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *);
doublereal safmin, safmax;
integer ioldsd[4];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer
*, integer *), xerbla_(char *, integer *),
zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *);
extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *,
integer *);
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *);
doublereal ulpinv;
integer lwkopt, mtypes, ntestt;
/* Fortran I/O blocks */
static cilist io___43 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___47 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___55 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___56 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___57 = { 0, 0, 0, fmt_9991, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* Purpose */
/* ======= */
/* ZDRVGG checks the nonsymmetric generalized eigenvalue driver */
/* routines. */
/* T T T */
/* ZGEGS factors A and B as Q S Z and Q T Z , where means */
/* transpose, T is upper triangular, S is in generalized Schur form */
/* (upper triangular), and Q and Z are unitary. It also */
/* computes the generalized eigenvalues (alpha(1),beta(1)), ..., */
/* (alpha(n),beta(n)), where alpha(j)=S(j,j) and beta(j)=T(j,j) -- */
/* thus, w(j) = alpha(j)/beta(j) is a root of the generalized */
/* eigenvalue problem */
/* det( A - w(j) B ) = 0 */
/* and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent */
/* problem */
/* det( m(j) A - B ) = 0 */
/* ZGEGV computes the generalized eigenvalues (alpha(1),beta(1)), ..., */
/* (alpha(n),beta(n)), the matrix L whose columns contain the */
/* generalized left eigenvectors l, and the matrix R whose columns */
/* contain the generalized right eigenvectors r for the pair (A,B). */
/* When ZDRVGG is called, a number of matrix "sizes" ("n's") and a */
/* number of matrix "types" are specified. For each size ("n") */
/* and each type of matrix, one matrix will be generated and used */
/* to test the nonsymmetric eigenroutines. For each matrix, 7 */
/* tests will be performed and compared with the threshhold THRESH: */
/* Results from ZGEGS: */
/* H */
/* (1) | A - Q S Z | / ( |A| n ulp ) */
/* H */
/* (2) | B - Q T Z | / ( |B| n ulp ) */
/* H */
/* (3) | I - QQ | / ( n ulp ) */
/* H */
/* (4) | I - ZZ | / ( n ulp ) */
/* (5) maximum over j of D(j) where: */
/* |alpha(j) - S(j,j)| |beta(j) - T(j,j)| */
/* D(j) = ------------------------ + ----------------------- */
/* max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) */
/* Results from ZGEGV: */
/* (6) max over all left eigenvalue/-vector pairs (beta/alpha,l) of */
/* | l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) ) */
/* where l**H is the conjugate tranpose of l. */
/* (7) max over all right eigenvalue/-vector pairs (beta/alpha,r) of */
/* | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) ) */
/* Test Matrices */
/* ---- -------- */
/* The sizes of the test matrices are specified by an array */
/* NN(1:NSIZES); the value of each element NN(j) specifies one size. */
/* The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if */
/* DOTYPE(j) is .TRUE., then matrix type "j" will be generated. */
/* Currently, the list of possible types is: */
/* (1) ( 0, 0 ) (a pair of zero matrices) */
/* (2) ( I, 0 ) (an identity and a zero matrix) */
/* (3) ( 0, I ) (an identity and a zero matrix) */
/* (4) ( I, I ) (a pair of identity matrices) */
/* t t */
/* (5) ( J , J ) (a pair of transposed Jordan blocks) */
/* t ( I 0 ) */
/* (6) ( X, Y ) where X = ( J 0 ) and Y = ( t ) */
/* ( 0 I ) ( 0 J ) */
/* and I is a k x k identity and J a (k+1)x(k+1) */
/* Jordan block; k=(N-1)/2 */
/* (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal */
/* matrix with those diagonal entries.) */
/* (8) ( I, D ) */
/* (9) ( big*D, small*I ) where "big" is near overflow and small=1/big */
/* (10) ( small*D, big*I ) */
/* (11) ( big*I, small*D ) */
/* (12) ( small*I, big*D ) */
/* (13) ( big*D, big*I ) */
/* (14) ( small*D, small*I ) */
/* (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and */
/* D2 is diag( 0, N-3, N-4,..., 1, 0, 0 ) */
/* t t */
/* (16) Q ( J , J ) Z where Q and Z are random unitary matrices. */
/* (17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices */
/* with random O(1) entries above the diagonal */
/* and diagonal entries diag(T1) = */
/* ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = */
/* ( 0, N-3, N-4,..., 1, 0, 0 ) */
/* (18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) */
/* s = machine precision. */
/* (19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 ) */
/* N-5 */
/* (20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) */
/* (21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) */
/* where r1,..., r(N-4) are random. */
/* (22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular */
/* matrices. */
/* Arguments */
/* ========= */
/* NSIZES (input) INTEGER */
/* The number of sizes of matrices to use. If it is zero, */
/* ZDRVGG does nothing. It must be at least zero. */
/* NN (input) INTEGER array, dimension (NSIZES) */
/* An array containing the sizes to be used for the matrices. */
/* Zero values will be skipped. The values must be at least */
/* zero. */
/* NTYPES (input) INTEGER */
/* The number of elements in DOTYPE. If it is zero, ZDRVGG */
/* does nothing. It must be at least zero. If it is MAXTYP+1 */
/* and NSIZES is 1, then an additional type, MAXTYP+1 is */
/* defined, which is to use whatever matrix is in A. This */
/* is only useful if DOTYPE(1:MAXTYP) is .FALSE. and */
/* DOTYPE(MAXTYP+1) is .TRUE. . */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* If DOTYPE(j) is .TRUE., then for each size in NN a */
/* matrix of that size and of type j will be generated. */
/* If NTYPES is smaller than the maximum number of types */
/* defined (PARAMETER MAXTYP), then types NTYPES+1 through */
/* MAXTYP will not be generated. If NTYPES is larger */
/* than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) */
/* will be ignored. */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry ISEED specifies the seed of the random number */
/* generator. The array elements should be between 0 and 4095; */
/* if not they will be reduced mod 4096. Also, ISEED(4) must */
/* be odd. The random number generator uses a linear */
/* congruential sequence limited to small integers, and so */
/* should produce machine independent random numbers. The */
/* values of ISEED are changed on exit, and can be used in the */
/* next call to ZDRVGG to continue the same random number */
/* sequence. */
/* THRESH (input) DOUBLE PRECISION */
/* A test will count as "failed" if the "error", computed as */
/* described above, exceeds THRESH. Note that the error is */
/* scaled to be O(1), so THRESH should be a reasonably small */
/* multiple of 1, e.g., 10 or 100. In particular, it should */
/* not depend on the precision (single vs. double) or the size */
/* of the matrix. It must be at least zero. */
/* THRSHN (input) DOUBLE PRECISION */
/* Threshhold for reporting eigenvector normalization error. */
/* If the normalization of any eigenvector differs from 1 by */
/* more than THRSHN*ulp, then a special error message will be */
/* printed. (This is handled separately from the other tests, */
/* since only a compiler or programming error should cause an */
/* error message, at least if THRSHN is at least 5--10.) */
/* NOUNIT (input) INTEGER */
/* The FORTRAN unit number for printing out error messages */
/* (e.g., if a routine returns IINFO not equal to 0.) */
/* A (input/workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* Used to hold the original A matrix. Used as input only */
/* if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and */
/* DOTYPE(MAXTYP+1)=.TRUE. */
/* LDA (input) INTEGER */
/* The leading dimension of A, B, S, T, S2, and T2. */
/* It must be at least 1 and at least max( NN ). */
/* B (input/workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* Used to hold the original B matrix. Used as input only */
/* if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and */
/* DOTYPE(MAXTYP+1)=.TRUE. */
/* S (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* The upper triangular matrix computed from A by ZGEGS. */
/* T (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* The upper triangular matrix computed from B by ZGEGS. */
/* S2 (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* The matrix computed from A by ZGEGV. This will be the */
/* Schur (upper triangular) form of some matrix related to A, */
/* but will not, in general, be the same as S. */
/* T2 (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* The matrix computed from B by ZGEGV. This will be the */
/* Schur form of some matrix related to B, but will not, in */
/* general, be the same as T. */
/* Q (workspace) COMPLEX*16 array, dimension (LDQ, max(NN)) */
/* The (left) unitary matrix computed by ZGEGS. */
/* LDQ (input) INTEGER */
/* The leading dimension of Q, Z, VL, and VR. It must */
/* be at least 1 and at least max( NN ). */
/* Z (workspace) COMPLEX*16 array, dimension (LDQ, max(NN)) */
/* The (right) unitary matrix computed by ZGEGS. */
/* ALPHA1 (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* BETA1 (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* The generalized eigenvalues of (A,B) computed by ZGEGS. */
/* ALPHA1(k) / BETA1(k) is the k-th generalized eigenvalue of */
/* the matrices in A and B. */
/* ALPHA2 (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* BETA2 (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* The generalized eigenvalues of (A,B) computed by ZGEGV. */
/* ALPHA2(k) / BETA2(k) is the k-th generalized eigenvalue of */
/* the matrices in A and B. */
/* VL (workspace) COMPLEX*16 array, dimension (LDQ, max(NN)) */
/* The (lower triangular) left eigenvector matrix for the */
/* matrices in A and B. */
/* VR (workspace) COMPLEX*16 array, dimension (LDQ, max(NN)) */
/* The (upper triangular) right eigenvector matrix for the */
/* matrices in A and B. */
/* WORK (workspace) COMPLEX*16 array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The number of entries in WORK. This must be at least */
/* MAX( 2*N, N*(NB+1), (k+1)*(2*k+N+1) ), where "k" is the */
/* sum of the blocksize and number-of-shifts for ZHGEQZ, and */
/* NB is the greatest of the blocksizes for ZGEQRF, ZUNMQR, */
/* and ZUNGQR. (The blocksizes and the number-of-shifts are */
/* retrieved through calls to ILAENV.) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (8*N) */
/* RESULT (output) DOUBLE PRECISION array, dimension (7) */
/* The values computed by the tests described above. */
/* The values are currently limited to 1/ulp, to avoid */
/* overflow. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: A routine returned an error code. INFO is the */
/* absolute value of the INFO value returned. */
/* ===================================================================== */
/* .. */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--nn;
--dotype;
--iseed;
t2_dim1 = *lda;
t2_offset = 1 + t2_dim1;
t2 -= t2_offset;
s2_dim1 = *lda;
s2_offset = 1 + s2_dim1;
s2 -= s2_offset;
t_dim1 = *lda;
t_offset = 1 + t_dim1;
t -= t_offset;
s_dim1 = *lda;
s_offset = 1 + s_dim1;
s -= s_offset;
b_dim1 = *lda;
b_offset = 1 + b_dim1;
b -= b_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
vr_dim1 = *ldq;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
vl_dim1 = *ldq;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
z_dim1 = *ldq;
z_offset = 1 + z_dim1;
z__ -= z_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--alpha1;
--beta1;
--alpha2;
--beta2;
--work;
--rwork;
--result;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
*info = 0;
badnn = FALSE_;
nmax = 1;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = nmax, i__3 = nn[j];
nmax = max(i__2,i__3);
if (nn[j] < 0) {
badnn = TRUE_;
}
/* L10: */
}
/* Maximum blocksize and shift -- we assume that blocksize and number */
/* of shifts are monotone increasing functions of N. */
/* Computing MAX */
i__1 = 1, i__2 = ilaenv_(&c__1, "ZGEQRF", " ", &nmax, &nmax, &c_n1, &c_n1), i__1 = max(i__1,i__2), i__2 = ilaenv_(&
c__1, "ZUNMQR", "LC", &nmax, &nmax, &nmax, &c_n1), i__1 = max(i__1,i__2), i__2 = ilaenv_(&c__1, "ZUNGQR",
" ", &nmax, &nmax, &nmax, &c_n1);
nb = max(i__1,i__2);
nbz = ilaenv_(&c__1, "ZHGEQZ", "SII", &nmax, &c__1, &nmax, &c__0);
ns = ilaenv_(&c__4, "ZHGEQZ", "SII", &nmax, &c__1, &nmax, &c__0);
i1 = nbz + ns;
/* Computing MAX */
i__1 = nmax << 1, i__2 = nmax * (nb + 1), i__1 = max(i__1,i__2), i__2 = ((
i1 << 1) + nmax + 1) * (i1 + 1);
lwkopt = max(i__1,i__2);
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badnn) {
*info = -2;
} else if (*ntypes < 0) {
*info = -3;
} else if (*thresh < 0.) {
*info = -6;
} else if (*lda <= 1 || *lda < nmax) {
*info = -10;
} else if (*ldq <= 1 || *ldq < nmax) {
*info = -19;
} else if (lwkopt > *lwork) {
*info = -30;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZDRVGG", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
ulp = dlamch_("Precision");
safmin = dlamch_("Safe minimum");
safmin /= ulp;
safmax = 1. / safmin;
dlabad_(&safmin, &safmax);
ulpinv = 1. / ulp;
/* The values RMAGN(2:3) depend on N, see below. */
rmagn[0] = 0.;
rmagn[1] = 1.;
/* Loop over sizes, types */
ntestt = 0;
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
n1 = max(1,n);
rmagn[2] = safmax * ulp / (doublereal) n1;
rmagn[3] = safmin * ulpinv * n1;
if (*nsizes != 1) {
mtypes = min(26,*ntypes);
} else {
mtypes = min(27,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L150;
}
++nmats;
ntest = 0;
/* Save ISEED in case of an error. */
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
/* Initialize RESULT */
for (j = 1; j <= 7; ++j) {
result[j] = 0.;
/* L30: */
}
/* Compute A and B */
/* Description of control parameters: */
/* KZLASS: =1 means w/o rotation, =2 means w/ rotation, */
/* =3 means random. */
/* KATYPE: the "type" to be passed to ZLATM4 for computing A. */
/* KAZERO: the pattern of zeros on the diagonal for A: */
/* =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ), */
/* =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ), */
/* =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of */
/* non-zero entries.) */
/* KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1), */
/* =2: large, =3: small. */
/* LASIGN: .TRUE. if the diagonal elements of A are to be */
/* multiplied by a random magnitude 1 number. */
/* KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B. */
/* KTRIAN: =0: don't fill in the upper triangle, =1: do. */
/* KZ1, KZ2, KADD: used to implement KAZERO and KBZERO. */
/* RMAGN: used to implement KAMAGN and KBMAGN. */
if (mtypes > 26) {
goto L110;
}
iinfo = 0;
if (kclass[jtype - 1] < 3) {
/* Generate A (w/o rotation) */
if ((i__3 = katype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
zlaset_("Full", &n, &n, &c_b1, &c_b1, &a[a_offset],
lda);
}
} else {
in = n;
}
zlatm4_(&katype[jtype - 1], &in, &kz1[kazero[jtype - 1] - 1],
&kz2[kazero[jtype - 1] - 1], &lasign[jtype - 1], &
rmagn[kamagn[jtype - 1]], &ulp, &rmagn[ktrian[jtype -
1] * kamagn[jtype - 1]], &c__2, &iseed[1], &a[
a_offset], lda);
iadd = kadd[kazero[jtype - 1] - 1];
if (iadd > 0 && iadd <= n) {
i__3 = iadd + iadd * a_dim1;
i__4 = kamagn[jtype - 1];
a[i__3].r = rmagn[i__4], a[i__3].i = 0.;
}
/* Generate B (w/o rotation) */
if ((i__3 = kbtype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
zlaset_("Full", &n, &n, &c_b1, &c_b1, &b[b_offset],
lda);
}
} else {
in = n;
}
zlatm4_(&kbtype[jtype - 1], &in, &kz1[kbzero[jtype - 1] - 1],
&kz2[kbzero[jtype - 1] - 1], &lbsign[jtype - 1], &
rmagn[kbmagn[jtype - 1]], &c_b39, &rmagn[ktrian[jtype
- 1] * kbmagn[jtype - 1]], &c__2, &iseed[1], &b[
b_offset], lda);
iadd = kadd[kbzero[jtype - 1] - 1];
if (iadd != 0 && iadd <= n) {
i__3 = iadd + iadd * b_dim1;
i__4 = kbmagn[jtype - 1];
b[i__3].r = rmagn[i__4], b[i__3].i = 0.;
}
if (kclass[jtype - 1] == 2 && n > 0) {
/* Include rotations */
/* Generate Q, Z as Householder transformations times */
/* a diagonal matrix. */
i__3 = n - 1;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = jc; jr <= i__4; ++jr) {
i__5 = jr + jc * q_dim1;
zlarnd_(&z__1, &c__3, &iseed[1]);
q[i__5].r = z__1.r, q[i__5].i = z__1.i;
i__5 = jr + jc * z_dim1;
zlarnd_(&z__1, &c__3, &iseed[1]);
z__[i__5].r = z__1.r, z__[i__5].i = z__1.i;
/* L40: */
}
i__4 = n + 1 - jc;
zlarfg_(&i__4, &q[jc + jc * q_dim1], &q[jc + 1 + jc *
q_dim1], &c__1, &work[jc]);
i__4 = (n << 1) + jc;
i__5 = jc + jc * q_dim1;
d__2 = q[i__5].r;
d__1 = d_sign(&c_b39, &d__2);
work[i__4].r = d__1, work[i__4].i = 0.;
i__4 = jc + jc * q_dim1;
q[i__4].r = 1., q[i__4].i = 0.;
i__4 = n + 1 - jc;
zlarfg_(&i__4, &z__[jc + jc * z_dim1], &z__[jc + 1 +
jc * z_dim1], &c__1, &work[n + jc]);
i__4 = n * 3 + jc;
i__5 = jc + jc * z_dim1;
d__2 = z__[i__5].r;
d__1 = d_sign(&c_b39, &d__2);
work[i__4].r = d__1, work[i__4].i = 0.;
i__4 = jc + jc * z_dim1;
z__[i__4].r = 1., z__[i__4].i = 0.;
/* L50: */
}
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__3 = n + n * q_dim1;
q[i__3].r = 1., q[i__3].i = 0.;
i__3 = n;
work[i__3].r = 0., work[i__3].i = 0.;
i__3 = n * 3;
d__1 = z_abs(&ctemp);
z__1.r = ctemp.r / d__1, z__1.i = ctemp.i / d__1;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__3 = n + n * z_dim1;
z__[i__3].r = 1., z__[i__3].i = 0.;
i__3 = n << 1;
work[i__3].r = 0., work[i__3].i = 0.;
i__3 = n << 2;
d__1 = z_abs(&ctemp);
z__1.r = ctemp.r / d__1, z__1.i = ctemp.i / d__1;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
/* Apply the diagonal matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = jr + jc * a_dim1;
i__6 = (n << 1) + jr;
d_cnjg(&z__3, &work[n * 3 + jc]);
z__2.r = work[i__6].r * z__3.r - work[i__6].i *
z__3.i, z__2.i = work[i__6].r * z__3.i +
work[i__6].i * z__3.r;
i__7 = jr + jc * a_dim1;
z__1.r = z__2.r * a[i__7].r - z__2.i * a[i__7].i,
z__1.i = z__2.r * a[i__7].i + z__2.i * a[
i__7].r;
a[i__5].r = z__1.r, a[i__5].i = z__1.i;
i__5 = jr + jc * b_dim1;
i__6 = (n << 1) + jr;
d_cnjg(&z__3, &work[n * 3 + jc]);
z__2.r = work[i__6].r * z__3.r - work[i__6].i *
z__3.i, z__2.i = work[i__6].r * z__3.i +
work[i__6].i * z__3.r;
i__7 = jr + jc * b_dim1;
z__1.r = z__2.r * b[i__7].r - z__2.i * b[i__7].i,
z__1.i = z__2.r * b[i__7].i + z__2.i * b[
i__7].r;
b[i__5].r = z__1.r, b[i__5].i = z__1.i;
/* L60: */
}
/* L70: */
}
i__3 = n - 1;
zunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &a[a_offset], lda, &work[(n << 1) + 1], &
iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
zunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &a[a_offset], lda, &work[(n << 1) +
1], &iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
zunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &b[b_offset], lda, &work[(n << 1) + 1], &
iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
zunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &b[b_offset], lda, &work[(n << 1) +
1], &iinfo);
if (iinfo != 0) {
goto L100;
}
}
} else {
/* Random matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = jr + jc * a_dim1;
i__6 = kamagn[jtype - 1];
zlarnd_(&z__2, &c__4, &iseed[1]);
z__1.r = rmagn[i__6] * z__2.r, z__1.i = rmagn[i__6] *
z__2.i;
a[i__5].r = z__1.r, a[i__5].i = z__1.i;
i__5 = jr + jc * b_dim1;
i__6 = kbmagn[jtype - 1];
zlarnd_(&z__2, &c__4, &iseed[1]);
z__1.r = rmagn[i__6] * z__2.r, z__1.i = rmagn[i__6] *
z__2.i;
b[i__5].r = z__1.r, b[i__5].i = z__1.i;
/* L80: */
}
/* L90: */
}
}
L100:
if (iinfo != 0) {
io___43.ciunit = *nounit;
s_wsfe(&io___43);
do_fio(&c__1, "Generator", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
return 0;
}
L110:
/* Call ZGEGS to compute H, T, Q, Z, alpha, and beta. */
zlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
zlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
ntest = 1;
result[1] = ulpinv;
zgegs_("V", "V", &n, &s[s_offset], lda, &t[t_offset], lda, &
alpha1[1], &beta1[1], &q[q_offset], ldq, &z__[z_offset],
ldq, &work[1], lwork, &rwork[1], &iinfo);
if (iinfo != 0) {
io___44.ciunit = *nounit;
s_wsfe(&io___44);
do_fio(&c__1, "ZGEGS", (ftnlen)5);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L130;
}
ntest = 4;
/* Do tests 1--4 */
zget51_(&c__1, &n, &a[a_offset], lda, &s[s_offset], lda, &q[
q_offset], ldq, &z__[z_offset], ldq, &work[1], &rwork[1],
&result[1]);
zget51_(&c__1, &n, &b[b_offset], lda, &t[t_offset], lda, &q[
q_offset], ldq, &z__[z_offset], ldq, &work[1], &rwork[1],
&result[2]);
zget51_(&c__3, &n, &b[b_offset], lda, &t[t_offset], lda, &q[
q_offset], ldq, &q[q_offset], ldq, &work[1], &rwork[1], &
result[3]);
zget51_(&c__3, &n, &b[b_offset], lda, &t[t_offset], lda, &z__[
z_offset], ldq, &z__[z_offset], ldq, &work[1], &rwork[1],
&result[4]);
/* Do test 5: compare eigenvalues with diagonals. */
temp1 = 0.;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = j;
i__5 = j + j * s_dim1;
z__2.r = alpha1[i__4].r - s[i__5].r, z__2.i = alpha1[i__4].i
- s[i__5].i;
z__1.r = z__2.r, z__1.i = z__2.i;
i__6 = j;
i__7 = j + j * t_dim1;
z__4.r = beta1[i__6].r - t[i__7].r, z__4.i = beta1[i__6].i -
t[i__7].i;
z__3.r = z__4.r, z__3.i = z__4.i;
/* Computing MAX */
i__8 = j;
i__9 = j + j * s_dim1;
d__13 = safmin, d__14 = (d__1 = alpha1[i__8].r, abs(d__1)) + (
d__2 = d_imag(&alpha1[j]), abs(d__2)), d__13 = max(
d__13,d__14), d__14 = (d__3 = s[i__9].r, abs(d__3)) +
(d__4 = d_imag(&s[j + j * s_dim1]), abs(d__4));
/* Computing MAX */
i__10 = j;
i__11 = j + j * t_dim1;
d__15 = safmin, d__16 = (d__5 = beta1[i__10].r, abs(d__5)) + (
d__6 = d_imag(&beta1[j]), abs(d__6)), d__15 = max(
d__15,d__16), d__16 = (d__7 = t[i__11].r, abs(d__7))
+ (d__8 = d_imag(&t[j + j * t_dim1]), abs(d__8));
temp2 = (((d__9 = z__1.r, abs(d__9)) + (d__10 = d_imag(&z__1),
abs(d__10))) / max(d__13,d__14) + ((d__11 = z__3.r,
abs(d__11)) + (d__12 = d_imag(&z__3), abs(d__12))) /
max(d__15,d__16)) / ulp;
temp1 = max(temp1,temp2);
/* L120: */
}
result[5] = temp1;
/* Call ZGEGV to compute S2, T2, VL, and VR, do tests. */
/* Eigenvalues and Eigenvectors */
zlacpy_(" ", &n, &n, &a[a_offset], lda, &s2[s2_offset], lda);
zlacpy_(" ", &n, &n, &b[b_offset], lda, &t2[t2_offset], lda);
ntest = 6;
result[6] = ulpinv;
zgegv_("V", "V", &n, &s2[s2_offset], lda, &t2[t2_offset], lda, &
alpha2[1], &beta2[1], &vl[vl_offset], ldq, &vr[vr_offset],
ldq, &work[1], lwork, &rwork[1], &iinfo);
if (iinfo != 0) {
io___47.ciunit = *nounit;
s_wsfe(&io___47);
do_fio(&c__1, "ZGEGV", (ftnlen)5);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L130;
}
ntest = 7;
/* Do Tests 6 and 7 */
zget52_(&c_true, &n, &a[a_offset], lda, &b[b_offset], lda, &vl[
vl_offset], ldq, &alpha2[1], &beta2[1], &work[1], &rwork[
1], dumma);
result[6] = dumma[0];
if (dumma[1] > *thrshn) {
io___49.ciunit = *nounit;
s_wsfe(&io___49);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "ZGEGV", (ftnlen)5);
do_fio(&c__1, (char *)&dumma[1], (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
zget52_(&c_false, &n, &a[a_offset], lda, &b[b_offset], lda, &vr[
vr_offset], ldq, &alpha2[1], &beta2[1], &work[1], &rwork[
1], dumma);
result[7] = dumma[0];
if (dumma[1] > *thresh) {
io___50.ciunit = *nounit;
s_wsfe(&io___50);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "ZGEGV", (ftnlen)5);
do_fio(&c__1, (char *)&dumma[1], (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L130:
ntestt += ntest;
/* Print out tests which fail. */
i__3 = ntest;
for (jr = 1; jr <= i__3; ++jr) {
if (result[jr] >= *thresh) {
/* If this is the first test to fail, */
/* print a header to the data file. */
if (nerrs == 0) {
io___51.ciunit = *nounit;
s_wsfe(&io___51);
do_fio(&c__1, "ZGG", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___52.ciunit = *nounit;
s_wsfe(&io___52);
e_wsfe();
io___53.ciunit = *nounit;
s_wsfe(&io___53);
e_wsfe();
io___54.ciunit = *nounit;
s_wsfe(&io___54);
do_fio(&c__1, "Unitary", (ftnlen)7);
e_wsfe();
/* Tests performed */
io___55.ciunit = *nounit;
s_wsfe(&io___55);
do_fio(&c__1, "unitary", (ftnlen)7);
do_fio(&c__1, "*", (ftnlen)1);
do_fio(&c__1, "conjugate transpose", (ftnlen)19);
for (j = 1; j <= 5; ++j) {
do_fio(&c__1, "*", (ftnlen)1);
}
e_wsfe();
}
++nerrs;
if (result[jr] < 1e4) {
io___56.ciunit = *nounit;
s_wsfe(&io___56);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
} else {
io___57.ciunit = *nounit;
s_wsfe(&io___57);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
}
}
/* L140: */
}
L150:
;
}
/* L160: */
}
/* Summary */
alasvm_("ZGG", nounit, &nerrs, &ntestt, &c__0);
return 0;
/* End of ZDRVGG */
} /* zdrvgg_ */
/* Subroutine */ int zdrgev_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, doublereal *thresh, integer *nounit,
doublecomplex *a, integer *lda, doublecomplex *b, doublecomplex *s,
doublecomplex *t, doublecomplex *q, integer *ldq, doublecomplex *z__,
doublecomplex *qe, integer *ldqe, doublecomplex *alpha, doublecomplex
*beta, doublecomplex *alpha1, doublecomplex *beta1, doublecomplex *
work, integer *lwork, doublereal *rwork, doublereal *result, integer *
info)
{
/* Initialized data */
static integer kclass[26] = { 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,2,3 };
static integer kbmagn[26] = { 1,1,1,1,1,1,1,1,3,2,3,2,2,3,1,1,1,1,1,1,1,3,
2,3,2,1 };
static integer ktrian[26] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,
1,1,1,1 };
static logical lasign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
TRUE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,TRUE_,TRUE_,FALSE_ };
static logical lbsign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_ };
static integer kz1[6] = { 0,1,2,1,3,3 };
static integer kz2[6] = { 0,0,1,2,1,1 };
static integer kadd[6] = { 0,0,0,0,3,2 };
static integer katype[26] = { 0,1,0,1,2,3,4,1,4,4,1,1,4,4,4,2,4,5,8,7,9,4,
4,4,4,0 };
static integer kbtype[26] = { 0,0,1,1,2,-3,1,4,1,1,4,4,1,1,-4,2,-4,8,8,8,
8,8,8,8,8,0 };
static integer kazero[26] = { 1,1,1,1,1,1,2,1,2,2,1,1,2,2,3,1,3,5,5,5,5,3,
3,3,3,1 };
static integer kbzero[26] = { 1,1,1,1,1,1,1,2,1,1,2,2,1,1,4,1,4,6,6,6,6,4,
4,4,4,1 };
static integer kamagn[26] = { 1,1,1,1,1,1,1,1,2,3,2,3,2,3,1,1,1,1,1,1,1,2,
3,3,2,1 };
/* Format strings */
static char fmt_9999[] = "(\002 ZDRGEV: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/3x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
"(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9998[] = "(\002 ZDRGEV: \002,a,\002 Eigenvectors from"
" \002,a,\002 incorrectly \002,\002normalized.\002,/\002 Bits of "
"error=\002,0p,g10.3,\002,\002,3x,\002N=\002,i4,\002, JTYPE=\002,"
"i3,\002, ISEED=(\002,3(i4,\002,\002),i5,\002)\002)";
static char fmt_9997[] = "(/1x,a3,\002 -- Complex Generalized eigenvalue"
" problem \002,\002driver\002)";
static char fmt_9996[] = "(\002 Matrix types (see ZDRGEV for details):"
" \002)";
static char fmt_9995[] = "(\002 Special Matrices:\002,23x,\002(J'=transp"
"osed Jordan block)\002,/\002 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I"
") 5=(J',J') \002,\0026=(diag(J',I), diag(I,J'))\002,/\002 Diag"
"onal Matrices: ( \002,\002D=diag(0,1,2,...) )\002,/\002 7=(D,"
"I) 9=(large*D, small*I\002,\002) 11=(large*I, small*D) 13=(l"
"arge*D, large*I)\002,/\002 8=(I,D) 10=(small*D, large*I) 12="
"(small*I, large*D) \002,\002 14=(small*D, small*I)\002,/\002 15"
"=(D, reversed D)\002)";
static char fmt_9994[] = "(\002 Matrices Rotated by Random \002,a,\002 M"
"atrices U, V:\002,/\002 16=Transposed Jordan Blocks "
" 19=geometric \002,\002alpha, beta=0,1\002,/\002 17=arithm. alp"
"ha&beta \002,\002 20=arithmetic alpha, beta=0,"
"1\002,/\002 18=clustered \002,\002alpha, beta=0,1 21"
"=random alpha, beta=0,1\002,/\002 Large & Small Matrices:\002,"
"/\002 22=(large, small) \002,\00223=(small,large) 24=(smal"
"l,small) 25=(large,large)\002,/\002 26=random O(1) matrices"
".\002)";
static char fmt_9993[] = "(/\002 Tests performed: \002,/\002 1 = max "
"| ( b A - a B )'*l | / const.,\002,/\002 2 = | |VR(i)| - 1 | / u"
"lp,\002,/\002 3 = max | ( b A - a B )*r | / const.\002,/\002 4 ="
" | |VL(i)| - 1 | / ulp,\002,/\002 5 = 0 if W same no matter if r"
" or l computed,\002,/\002 6 = 0 if l same no matter if l compute"
"d,\002,/\002 7 = 0 if r same no matter if r computed,\002,/1x)";
static char fmt_9992[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i2,\002 is\002"
",0p,f8.2)";
static char fmt_9991[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i2,\002 is\002"
",1p,d10.3)";
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, qe_dim1,
qe_offset, s_dim1, s_offset, t_dim1, t_offset, z_dim1, z_offset,
i__1, i__2, i__3, i__4, i__5, i__6, i__7;
doublereal d__1, d__2;
doublecomplex z__1, z__2, z__3;
/* Builtin functions */
double d_sign(doublereal *, doublereal *), z_abs(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
static integer iadd, ierr, nmax, i__, j, n;
static logical badnn;
static doublereal rmagn[4];
static doublecomplex ctemp;
extern /* Subroutine */ int zget52_(logical *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *
, doublecomplex *, doublecomplex *, doublecomplex *, doublereal *,
doublereal *);
static integer nmats, jsize;
extern /* Subroutine */ int zggev_(char *, char *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *);
static integer nerrs, jtype, n1;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), zlatm4_(
integer *, integer *, integer *, integer *, logical *, doublereal
*, doublereal *, doublereal *, integer *, integer *,
doublecomplex *, integer *);
static integer jc, nb, in;
extern doublereal dlamch_(char *);
static integer jr;
extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *);
static doublereal safmin, safmax;
static integer ioldsd[4];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer
*, integer *), xerbla_(char *, integer *),
zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *);
extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *,
integer *);
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *);
static integer minwrk, maxwrk;
static doublereal ulpinv;
static integer mtypes, ntestt;
static doublereal ulp;
/* Fortran I/O blocks */
static cilist io___40 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___46 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___47 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___48 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9991, 0 };
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define q_subscr(a_1,a_2) (a_2)*q_dim1 + a_1
#define q_ref(a_1,a_2) q[q_subscr(a_1,a_2)]
#define z___subscr(a_1,a_2) (a_2)*z_dim1 + a_1
#define z___ref(a_1,a_2) z__[z___subscr(a_1,a_2)]
#define qe_subscr(a_1,a_2) (a_2)*qe_dim1 + a_1
#define qe_ref(a_1,a_2) qe[qe_subscr(a_1,a_2)]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZDRGEV checks the nonsymmetric generalized eigenvalue problem driver
routine ZGGEV.
ZGGEV computes for a pair of n-by-n nonsymmetric matrices (A,B) the
generalized eigenvalues and, optionally, the left and right
eigenvectors.
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
or a ratio alpha/beta = w, such that A - w*B is singular. It is
usually represented as the pair (alpha,beta), as there is reasonalbe
interpretation for beta=0, and even for both being zero.
A right generalized eigenvector corresponding to a generalized
eigenvalue w for a pair of matrices (A,B) is a vector r such that
(A - wB) * r = 0. A left generalized eigenvector is a vector l such
that l**H * (A - wB) = 0, where l**H is the conjugate-transpose of l.
When ZDRGEV is called, a number of matrix "sizes" ("n's") and a
number of matrix "types" are specified. For each size ("n")
and each type of matrix, a pair of matrices (A, B) will be generated
and used for testing. For each matrix pair, the following tests
will be performed and compared with the threshhold THRESH.
Results from ZGGEV:
(1) max over all left eigenvalue/-vector pairs (alpha/beta,l) of
| VL**H * (beta A - alpha B) |/( ulp max(|beta A|, |alpha B|) )
where VL**H is the conjugate-transpose of VL.
(2) | |VL(i)| - 1 | / ulp and whether largest component real
VL(i) denotes the i-th column of VL.
(3) max over all left eigenvalue/-vector pairs (alpha/beta,r) of
| (beta A - alpha B) * VR | / ( ulp max(|beta A|, |alpha B|) )
(4) | |VR(i)| - 1 | / ulp and whether largest component real
VR(i) denotes the i-th column of VR.
(5) W(full) = W(partial)
W(full) denotes the eigenvalues computed when both l and r
are also computed, and W(partial) denotes the eigenvalues
computed when only W, only W and r, or only W and l are
computed.
(6) VL(full) = VL(partial)
VL(full) denotes the left eigenvectors computed when both l
and r are computed, and VL(partial) denotes the result
when only l is computed.
(7) VR(full) = VR(partial)
VR(full) denotes the right eigenvectors computed when both l
and r are also computed, and VR(partial) denotes the result
when only l is computed.
Test Matrices
---- --------
The sizes of the test matrices are specified by an array
NN(1:NSIZES); the value of each element NN(j) specifies one size.
The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if
DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
Currently, the list of possible types is:
(1) ( 0, 0 ) (a pair of zero matrices)
(2) ( I, 0 ) (an identity and a zero matrix)
(3) ( 0, I ) (an identity and a zero matrix)
(4) ( I, I ) (a pair of identity matrices)
t t
(5) ( J , J ) (a pair of transposed Jordan blocks)
t ( I 0 )
(6) ( X, Y ) where X = ( J 0 ) and Y = ( t )
( 0 I ) ( 0 J )
and I is a k x k identity and J a (k+1)x(k+1)
Jordan block; k=(N-1)/2
(7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal
matrix with those diagonal entries.)
(8) ( I, D )
(9) ( big*D, small*I ) where "big" is near overflow and small=1/big
(10) ( small*D, big*I )
(11) ( big*I, small*D )
(12) ( small*I, big*D )
(13) ( big*D, big*I )
(14) ( small*D, small*I )
(15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
t t
(16) Q ( J , J ) Z where Q and Z are random orthogonal matrices.
(17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices
with random O(1) entries above the diagonal
and diagonal entries diag(T1) =
( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
( 0, N-3, N-4,..., 1, 0, 0 )
(18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
s = machine precision.
(19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
N-5
(20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 )
diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
(21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
where r1,..., r(N-4) are random.
(22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
diag(T2) = ( 0, 1, ..., 1, 0, 0 )
(23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
diag(T2) = ( 0, 1, ..., 1, 0, 0 )
(24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
diag(T2) = ( 0, 1, ..., 1, 0, 0 )
(25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
diag(T2) = ( 0, 1, ..., 1, 0, 0 )
(26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
matrices.
Arguments
=========
NSIZES (input) INTEGER
The number of sizes of matrices to use. If it is zero,
ZDRGES does nothing. NSIZES >= 0.
NN (input) INTEGER array, dimension (NSIZES)
An array containing the sizes to be used for the matrices.
Zero values will be skipped. NN >= 0.
NTYPES (input) INTEGER
The number of elements in DOTYPE. If it is zero, ZDRGEV
does nothing. It must be at least zero. If it is MAXTYP+1
and NSIZES is 1, then an additional type, MAXTYP+1 is
defined, which is to use whatever matrix is in A. This
is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
DOTYPE(MAXTYP+1) is .TRUE. .
DOTYPE (input) LOGICAL array, dimension (NTYPES)
If DOTYPE(j) is .TRUE., then for each size in NN a
matrix of that size and of type j will be generated.
If NTYPES is smaller than the maximum number of types
defined (PARAMETER MAXTYP), then types NTYPES+1 through
MAXTYP will not be generated. If NTYPES is larger
than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
will be ignored.
ISEED (input/output) INTEGER array, dimension (4)
On entry ISEED specifies the seed of the random number
generator. The array elements should be between 0 and 4095;
if not they will be reduced mod 4096. Also, ISEED(4) must
be odd. The random number generator uses a linear
congruential sequence limited to small integers, and so
should produce machine independent random numbers. The
values of ISEED are changed on exit, and can be used in the
next call to ZDRGES to continue the same random number
sequence.
THRESH (input) DOUBLE PRECISION
A test will count as "failed" if the "error", computed as
described above, exceeds THRESH. Note that the error is
scaled to be O(1), so THRESH should be a reasonably small
multiple of 1, e.g., 10 or 100. In particular, it should
not depend on the precision (single vs. double) or the size
of the matrix. It must be at least zero.
NOUNIT (input) INTEGER
The FORTRAN unit number for printing out error messages
(e.g., if a routine returns IERR not equal to 0.)
A (input/workspace) COMPLEX*16 array, dimension(LDA, max(NN))
Used to hold the original A matrix. Used as input only
if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
DOTYPE(MAXTYP+1)=.TRUE.
LDA (input) INTEGER
The leading dimension of A, B, S, and T.
It must be at least 1 and at least max( NN ).
B (input/workspace) COMPLEX*16 array, dimension(LDA, max(NN))
Used to hold the original B matrix. Used as input only
if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
DOTYPE(MAXTYP+1)=.TRUE.
S (workspace) COMPLEX*16 array, dimension (LDA, max(NN))
The Schur form matrix computed from A by ZGGEV. On exit, S
contains the Schur form matrix corresponding to the matrix
in A.
T (workspace) COMPLEX*16 array, dimension (LDA, max(NN))
The upper triangular matrix computed from B by ZGGEV.
Q (workspace) COMPLEX*16 array, dimension (LDQ, max(NN))
The (left) eigenvectors matrix computed by ZGGEV.
LDQ (input) INTEGER
The leading dimension of Q and Z. It must
be at least 1 and at least max( NN ).
Z (workspace) COMPLEX*16 array, dimension( LDQ, max(NN) )
The (right) orthogonal matrix computed by ZGGEV.
QE (workspace) COMPLEX*16 array, dimension( LDQ, max(NN) )
QE holds the computed right or left eigenvectors.
LDQE (input) INTEGER
The leading dimension of QE. LDQE >= max(1,max(NN)).
ALPHA (workspace) COMPLEX*16 array, dimension (max(NN))
BETA (workspace) COMPLEX*16 array, dimension (max(NN))
The generalized eigenvalues of (A,B) computed by ZGGEV.
( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th
generalized eigenvalue of A and B.
ALPHA1 (workspace) COMPLEX*16 array, dimension (max(NN))
BETA1 (workspace) COMPLEX*16 array, dimension (max(NN))
Like ALPHAR, ALPHAI, BETA, these arrays contain the
eigenvalues of A and B, but those computed when ZGGEV only
computes a partial eigendecomposition, i.e. not the
eigenvalues and left and right eigenvectors.
WORK (workspace) COMPLEX*16 array, dimension (LWORK)
LWORK (input) INTEGER
The number of entries in WORK. LWORK >= N*(N+1)
RWORK (workspace) DOUBLE PRECISION array, dimension (8*N)
Real workspace.
RESULT (output) DOUBLE PRECISION array, dimension (2)
The values computed by the tests described above.
The values are currently limited to 1/ulp, to avoid overflow.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: A routine returned an error code. INFO is the
absolute value of the INFO value returned.
=====================================================================
Parameter adjustments */
--nn;
--dotype;
--iseed;
t_dim1 = *lda;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
s_dim1 = *lda;
s_offset = 1 + s_dim1 * 1;
s -= s_offset;
b_dim1 = *lda;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
z_dim1 = *ldq;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
qe_dim1 = *ldqe;
qe_offset = 1 + qe_dim1 * 1;
qe -= qe_offset;
--alpha;
--beta;
--alpha1;
--beta1;
--work;
--rwork;
--result;
/* Function Body
Check for errors */
*info = 0;
badnn = FALSE_;
nmax = 1;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = nmax, i__3 = nn[j];
nmax = max(i__2,i__3);
if (nn[j] < 0) {
badnn = TRUE_;
}
/* L10: */
}
if (*nsizes < 0) {
*info = -1;
} else if (badnn) {
*info = -2;
} else if (*ntypes < 0) {
*info = -3;
} else if (*thresh < 0.) {
*info = -6;
} else if (*lda <= 1 || *lda < nmax) {
*info = -9;
} else if (*ldq <= 1 || *ldq < nmax) {
*info = -14;
} else if (*ldqe <= 1 || *ldqe < nmax) {
*info = -17;
}
/* Compute workspace
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
NB refers to the optimal block size for the immediately
following subroutine, as returned by ILAENV. */
minwrk = 1;
if (*info == 0 && *lwork >= 1) {
minwrk = nmax * (nmax + 1);
/* Computing MAX */
i__1 = 1, i__2 = ilaenv_(&c__1, "ZGEQRF", " ", &nmax, &nmax, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1), i__1 = max(i__1,i__2), i__2 =
ilaenv_(&c__1, "ZUNMQR", "LC", &nmax, &nmax, &nmax, &c_n1, (
ftnlen)6, (ftnlen)2), i__1 = max(i__1,i__2), i__2 = ilaenv_(&
c__1, "ZUNGQR", " ", &nmax, &nmax, &nmax, &c_n1, (ftnlen)6, (
ftnlen)1);
nb = max(i__1,i__2);
/* Computing MAX */
i__1 = nmax << 1, i__2 = nmax * (nb + 1), i__1 = max(i__1,i__2), i__2
= nmax * (nmax + 1);
maxwrk = max(i__1,i__2);
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
}
if (*lwork < minwrk) {
*info = -23;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZDRGEV", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
ulp = dlamch_("Precision");
safmin = dlamch_("Safe minimum");
safmin /= ulp;
safmax = 1. / safmin;
dlabad_(&safmin, &safmax);
ulpinv = 1. / ulp;
/* The values RMAGN(2:3) depend on N, see below. */
rmagn[0] = 0.;
rmagn[1] = 1.;
/* Loop over sizes, types */
ntestt = 0;
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
n1 = max(1,n);
rmagn[2] = safmax * ulp / (doublereal) n1;
rmagn[3] = safmin * ulpinv * n1;
if (*nsizes != 1) {
mtypes = min(26,*ntypes);
} else {
mtypes = min(27,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L210;
}
++nmats;
/* Save ISEED in case of an error. */
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
/* Generate test matrices A and B
Description of control parameters:
KZLASS: =1 means w/o rotation, =2 means w/ rotation,
=3 means random.
KATYPE: the "type" to be passed to ZLATM4 for computing A.
KAZERO: the pattern of zeros on the diagonal for A:
=1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
=4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
=6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of
non-zero entries.)
KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
=2: large, =3: small.
LASIGN: .TRUE. if the diagonal elements of A are to be
multiplied by a random magnitude 1 number.
KBTYPE, KBZERO, KBMAGN, LBSIGN: the same, but for B.
KTRIAN: =0: don't fill in the upper triangle, =1: do.
KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
RMAGN: used to implement KAMAGN and KBMAGN. */
if (mtypes > 26) {
goto L100;
}
ierr = 0;
if (kclass[jtype - 1] < 3) {
/* Generate A (w/o rotation) */
if ((i__3 = katype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
zlaset_("Full", &n, &n, &c_b1, &c_b1, &a[a_offset],
lda);
}
} else {
in = n;
}
zlatm4_(&katype[jtype - 1], &in, &kz1[kazero[jtype - 1] - 1],
&kz2[kazero[jtype - 1] - 1], &lasign[jtype - 1], &
rmagn[kamagn[jtype - 1]], &ulp, &rmagn[ktrian[jtype -
1] * kamagn[jtype - 1]], &c__2, &iseed[1], &a[
a_offset], lda);
iadd = kadd[kazero[jtype - 1] - 1];
if (iadd > 0 && iadd <= n) {
i__3 = a_subscr(iadd, iadd);
i__4 = kamagn[jtype - 1];
a[i__3].r = rmagn[i__4], a[i__3].i = 0.;
}
/* Generate B (w/o rotation) */
if ((i__3 = kbtype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
zlaset_("Full", &n, &n, &c_b1, &c_b1, &b[b_offset],
lda);
}
} else {
in = n;
}
zlatm4_(&kbtype[jtype - 1], &in, &kz1[kbzero[jtype - 1] - 1],
&kz2[kbzero[jtype - 1] - 1], &lbsign[jtype - 1], &
rmagn[kbmagn[jtype - 1]], &c_b28, &rmagn[ktrian[jtype
- 1] * kbmagn[jtype - 1]], &c__2, &iseed[1], &b[
b_offset], lda);
iadd = kadd[kbzero[jtype - 1] - 1];
if (iadd != 0 && iadd <= n) {
i__3 = b_subscr(iadd, iadd);
i__4 = kbmagn[jtype - 1];
b[i__3].r = rmagn[i__4], b[i__3].i = 0.;
}
if (kclass[jtype - 1] == 2 && n > 0) {
/* Include rotations
Generate Q, Z as Householder transformations times
a diagonal matrix. */
i__3 = n - 1;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = jc; jr <= i__4; ++jr) {
i__5 = q_subscr(jr, jc);
zlarnd_(&z__1, &c__3, &iseed[1]);
q[i__5].r = z__1.r, q[i__5].i = z__1.i;
i__5 = z___subscr(jr, jc);
zlarnd_(&z__1, &c__3, &iseed[1]);
z__[i__5].r = z__1.r, z__[i__5].i = z__1.i;
/* L30: */
}
i__4 = n + 1 - jc;
zlarfg_(&i__4, &q_ref(jc, jc), &q_ref(jc + 1, jc), &
c__1, &work[jc]);
i__4 = (n << 1) + jc;
i__5 = q_subscr(jc, jc);
d__2 = q[i__5].r;
d__1 = d_sign(&c_b28, &d__2);
work[i__4].r = d__1, work[i__4].i = 0.;
i__4 = q_subscr(jc, jc);
q[i__4].r = 1., q[i__4].i = 0.;
i__4 = n + 1 - jc;
zlarfg_(&i__4, &z___ref(jc, jc), &z___ref(jc + 1, jc),
&c__1, &work[n + jc]);
i__4 = n * 3 + jc;
i__5 = z___subscr(jc, jc);
d__2 = z__[i__5].r;
d__1 = d_sign(&c_b28, &d__2);
work[i__4].r = d__1, work[i__4].i = 0.;
i__4 = z___subscr(jc, jc);
z__[i__4].r = 1., z__[i__4].i = 0.;
/* L40: */
}
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__3 = q_subscr(n, n);
q[i__3].r = 1., q[i__3].i = 0.;
i__3 = n;
work[i__3].r = 0., work[i__3].i = 0.;
i__3 = n * 3;
d__1 = z_abs(&ctemp);
z__1.r = ctemp.r / d__1, z__1.i = ctemp.i / d__1;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__3 = z___subscr(n, n);
z__[i__3].r = 1., z__[i__3].i = 0.;
i__3 = n << 1;
work[i__3].r = 0., work[i__3].i = 0.;
i__3 = n << 2;
d__1 = z_abs(&ctemp);
z__1.r = ctemp.r / d__1, z__1.i = ctemp.i / d__1;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
/* Apply the diagonal matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = a_subscr(jr, jc);
i__6 = (n << 1) + jr;
d_cnjg(&z__3, &work[n * 3 + jc]);
z__2.r = work[i__6].r * z__3.r - work[i__6].i *
z__3.i, z__2.i = work[i__6].r * z__3.i +
work[i__6].i * z__3.r;
i__7 = a_subscr(jr, jc);
z__1.r = z__2.r * a[i__7].r - z__2.i * a[i__7].i,
z__1.i = z__2.r * a[i__7].i + z__2.i * a[
i__7].r;
a[i__5].r = z__1.r, a[i__5].i = z__1.i;
i__5 = b_subscr(jr, jc);
i__6 = (n << 1) + jr;
d_cnjg(&z__3, &work[n * 3 + jc]);
z__2.r = work[i__6].r * z__3.r - work[i__6].i *
z__3.i, z__2.i = work[i__6].r * z__3.i +
work[i__6].i * z__3.r;
i__7 = b_subscr(jr, jc);
z__1.r = z__2.r * b[i__7].r - z__2.i * b[i__7].i,
z__1.i = z__2.r * b[i__7].i + z__2.i * b[
i__7].r;
b[i__5].r = z__1.r, b[i__5].i = z__1.i;
/* L50: */
}
/* L60: */
}
i__3 = n - 1;
zunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &a[a_offset], lda, &work[(n << 1) + 1], &ierr);
if (ierr != 0) {
goto L90;
}
i__3 = n - 1;
zunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &a[a_offset], lda, &work[(n << 1) +
1], &ierr);
if (ierr != 0) {
goto L90;
}
i__3 = n - 1;
zunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &b[b_offset], lda, &work[(n << 1) + 1], &ierr);
if (ierr != 0) {
goto L90;
}
i__3 = n - 1;
zunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &b[b_offset], lda, &work[(n << 1) +
1], &ierr);
if (ierr != 0) {
goto L90;
}
}
} else {
/* Random matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = a_subscr(jr, jc);
i__6 = kamagn[jtype - 1];
zlarnd_(&z__2, &c__4, &iseed[1]);
z__1.r = rmagn[i__6] * z__2.r, z__1.i = rmagn[i__6] *
z__2.i;
a[i__5].r = z__1.r, a[i__5].i = z__1.i;
i__5 = b_subscr(jr, jc);
i__6 = kbmagn[jtype - 1];
zlarnd_(&z__2, &c__4, &iseed[1]);
z__1.r = rmagn[i__6] * z__2.r, z__1.i = rmagn[i__6] *
z__2.i;
b[i__5].r = z__1.r, b[i__5].i = z__1.i;
/* L70: */
}
/* L80: */
}
}
L90:
if (ierr != 0) {
io___40.ciunit = *nounit;
s_wsfe(&io___40);
do_fio(&c__1, "Generator", (ftnlen)9);
do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(ierr);
return 0;
}
L100:
for (i__ = 1; i__ <= 7; ++i__) {
result[i__] = -1.;
/* L110: */
}
/* Call ZGGEV to compute eigenvalues and eigenvectors. */
zlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
zlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
zggev_("V", "V", &n, &s[s_offset], lda, &t[t_offset], lda, &alpha[
1], &beta[1], &q[q_offset], ldq, &z__[z_offset], ldq, &
work[1], lwork, &rwork[1], &ierr);
if (ierr != 0 && ierr != n + 1) {
result[1] = ulpinv;
io___42.ciunit = *nounit;
s_wsfe(&io___42);
do_fio(&c__1, "ZGGEV1", (ftnlen)6);
do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(ierr);
goto L190;
}
/* Do the tests (1) and (2) */
zget52_(&c_true, &n, &a[a_offset], lda, &b[b_offset], lda, &q[
q_offset], ldq, &alpha[1], &beta[1], &work[1], &rwork[1],
&result[1]);
if (result[2] > *thresh) {
io___43.ciunit = *nounit;
s_wsfe(&io___43);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "ZGGEV1", (ftnlen)6);
do_fio(&c__1, (char *)&result[2], (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Do the tests (3) and (4) */
zget52_(&c_false, &n, &a[a_offset], lda, &b[b_offset], lda, &z__[
z_offset], ldq, &alpha[1], &beta[1], &work[1], &rwork[1],
&result[3]);
if (result[4] > *thresh) {
io___44.ciunit = *nounit;
s_wsfe(&io___44);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "ZGGEV1", (ftnlen)6);
do_fio(&c__1, (char *)&result[4], (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Do test (5) */
zlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
zlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
zggev_("N", "N", &n, &s[s_offset], lda, &t[t_offset], lda, &
alpha1[1], &beta1[1], &q[q_offset], ldq, &z__[z_offset],
ldq, &work[1], lwork, &rwork[1], &ierr);
if (ierr != 0 && ierr != n + 1) {
result[1] = ulpinv;
io___45.ciunit = *nounit;
s_wsfe(&io___45);
do_fio(&c__1, "ZGGEV2", (ftnlen)6);
do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(ierr);
goto L190;
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = j;
i__5 = j;
i__6 = j;
i__7 = j;
if (alpha[i__4].r != alpha1[i__5].r || alpha[i__4].i !=
alpha1[i__5].i || (beta[i__6].r != beta1[i__7].r ||
beta[i__6].i != beta1[i__7].i)) {
result[5] = ulpinv;
}
/* L120: */
}
/* Do test (6): Compute eigenvalues and left eigenvectors,
and test them */
zlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
zlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
zggev_("V", "N", &n, &s[s_offset], lda, &t[t_offset], lda, &
alpha1[1], &beta1[1], &qe[qe_offset], ldqe, &z__[z_offset]
, ldq, &work[1], lwork, &rwork[1], &ierr);
if (ierr != 0 && ierr != n + 1) {
result[1] = ulpinv;
io___46.ciunit = *nounit;
s_wsfe(&io___46);
do_fio(&c__1, "ZGGEV3", (ftnlen)6);
do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(ierr);
goto L190;
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = j;
i__5 = j;
i__6 = j;
i__7 = j;
if (alpha[i__4].r != alpha1[i__5].r || alpha[i__4].i !=
alpha1[i__5].i || (beta[i__6].r != beta1[i__7].r ||
beta[i__6].i != beta1[i__7].i)) {
result[6] = ulpinv;
}
/* L130: */
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = n;
for (jc = 1; jc <= i__4; ++jc) {
i__5 = q_subscr(j, jc);
i__6 = qe_subscr(j, jc);
if (q[i__5].r != qe[i__6].r || q[i__5].i != qe[i__6].i) {
result[6] = ulpinv;
}
/* L140: */
}
/* L150: */
}
/* Do test (7): Compute eigenvalues and right eigenvectors,
and test them */
zlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
zlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
zggev_("N", "V", &n, &s[s_offset], lda, &t[t_offset], lda, &
alpha1[1], &beta1[1], &q[q_offset], ldq, &qe[qe_offset],
ldqe, &work[1], lwork, &rwork[1], &ierr);
if (ierr != 0 && ierr != n + 1) {
result[1] = ulpinv;
io___47.ciunit = *nounit;
s_wsfe(&io___47);
do_fio(&c__1, "ZGGEV4", (ftnlen)6);
do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(ierr);
goto L190;
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = j;
i__5 = j;
i__6 = j;
i__7 = j;
if (alpha[i__4].r != alpha1[i__5].r || alpha[i__4].i !=
alpha1[i__5].i || (beta[i__6].r != beta1[i__7].r ||
beta[i__6].i != beta1[i__7].i)) {
result[7] = ulpinv;
}
/* L160: */
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = n;
for (jc = 1; jc <= i__4; ++jc) {
i__5 = z___subscr(j, jc);
i__6 = qe_subscr(j, jc);
if (z__[i__5].r != qe[i__6].r || z__[i__5].i != qe[i__6]
.i) {
result[7] = ulpinv;
}
/* L170: */
}
/* L180: */
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L190:
ntestt += 7;
/* Print out tests which fail. */
for (jr = 1; jr <= 9; ++jr) {
if (result[jr] >= *thresh) {
/* If this is the first test to fail,
print a header to the data file. */
if (nerrs == 0) {
io___48.ciunit = *nounit;
s_wsfe(&io___48);
do_fio(&c__1, "ZGV", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___49.ciunit = *nounit;
s_wsfe(&io___49);
e_wsfe();
io___50.ciunit = *nounit;
s_wsfe(&io___50);
e_wsfe();
io___51.ciunit = *nounit;
s_wsfe(&io___51);
do_fio(&c__1, "Orthogonal", (ftnlen)10);
e_wsfe();
/* Tests performed */
io___52.ciunit = *nounit;
s_wsfe(&io___52);
e_wsfe();
}
++nerrs;
if (result[jr] < 1e4) {
io___53.ciunit = *nounit;
s_wsfe(&io___53);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
} else {
io___54.ciunit = *nounit;
s_wsfe(&io___54);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
}
}
/* L200: */
}
L210:
;
}
/* L220: */
}
/* Summary */
alasvm_("ZGV", nounit, &nerrs, &ntestt, &c__0);
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
return 0;
/* End of ZDRGEV */
} /* zdrgev_ */
/* Subroutine */ int zlattb_(integer *imat, char *uplo, char *trans, char *
diag, integer *iseed, integer *n, integer *kd, doublecomplex *ab,
integer *ldab, doublecomplex *b, doublecomplex *work, doublereal *
rwork, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
double sqrt(doublereal);
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
double pow_dd(doublereal *, doublereal *), z_abs(doublecomplex *);
/* Local variables */
static doublereal sfac;
static integer ioff, mode, lenj;
static char path[3], dist[1];
static doublereal unfl, rexp;
static char type__[1];
static doublereal texp;
static doublecomplex star1, plus1, plus2;
static integer i__, j;
static doublereal bscal;
extern logical lsame_(char *, char *);
static doublereal tscal, anorm, bnorm, tleft;
static logical upper;
static doublereal tnorm;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zswap_(integer *, doublecomplex *,
integer *, doublecomplex *, integer *), zlatb4_(char *, integer *,
integer *, integer *, char *, integer *, integer *, doublereal *,
integer *, doublereal *, char *),
dlabad_(doublereal *, doublereal *);
static integer kl;
extern doublereal dlamch_(char *);
static integer ku, iy;
extern doublereal dlarnd_(integer *, integer *);
static char packit[1];
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *);
static doublereal bignum, cndnum;
extern /* Subroutine */ int dlarnv_(integer *, integer *, integer *,
doublereal *);
extern integer izamax_(integer *, doublecomplex *, integer *);
extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *,
integer *);
static integer jcount;
extern /* Subroutine */ int zlatms_(integer *, integer *, char *, integer
*, char *, doublereal *, integer *, doublereal *, doublereal *,
integer *, integer *, char *, doublecomplex *, integer *,
doublecomplex *, integer *);
static doublereal smlnum;
extern /* Subroutine */ int zlarnv_(integer *, integer *, integer *,
doublecomplex *);
static doublereal ulp;
#define ab_subscr(a_1,a_2) (a_2)*ab_dim1 + a_1
#define ab_ref(a_1,a_2) ab[ab_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
=======
ZLATTB generates a triangular test matrix in 2-dimensional storage.
IMAT and UPLO uniquely specify the properties of the test matrix,
which is returned in the array A.
Arguments
=========
IMAT (input) INTEGER
An integer key describing which matrix to generate for this
path.
UPLO (input) CHARACTER*1
Specifies whether the matrix A will be upper or lower
triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS (input) CHARACTER*1
Specifies whether the matrix or its transpose will be used.
= 'N': No transpose
= 'T': Transpose
= 'C': Conjugate transpose (= transpose)
DIAG (output) CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
ISEED (input/output) INTEGER array, dimension (4)
The seed vector for the random number generator (used in
ZLATMS). Modified on exit.
N (input) INTEGER
The order of the matrix to be generated.
KD (input) INTEGER
The number of superdiagonals or subdiagonals of the banded
triangular matrix A. KD >= 0.
AB (output) COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangular banded matrix A, stored in the
first KD+1 rows of AB. Let j be a column of A, 1<=j<=n.
If UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j.
If UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B (workspace) COMPLEX*16 array, dimension (N)
WORK (workspace) COMPLEX*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Parameter adjustments */
--iseed;
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1 * 1;
ab -= ab_offset;
--b;
--work;
--rwork;
/* Function Body */
s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "TB", (ftnlen)2, (ftnlen)2);
unfl = dlamch_("Safe minimum");
ulp = dlamch_("Epsilon") * dlamch_("Base");
smlnum = unfl;
bignum = (1. - ulp) / smlnum;
dlabad_(&smlnum, &bignum);
if (*imat >= 6 && *imat <= 9 || *imat == 17) {
*(unsigned char *)diag = 'U';
} else {
*(unsigned char *)diag = 'N';
}
*info = 0;
/* Quick return if N.LE.0. */
if (*n <= 0) {
return 0;
}
/* Call ZLATB4 to set parameters for CLATMS. */
upper = lsame_(uplo, "U");
if (upper) {
zlatb4_(path, imat, n, n, type__, &kl, &ku, &anorm, &mode, &cndnum,
dist);
ku = *kd;
/* Computing MAX */
i__1 = 0, i__2 = *kd - *n + 1;
ioff = max(i__1,i__2) + 1;
kl = 0;
*(unsigned char *)packit = 'Q';
} else {
i__1 = -(*imat);
zlatb4_(path, &i__1, n, n, type__, &kl, &ku, &anorm, &mode, &cndnum,
dist);
kl = *kd;
ioff = 1;
ku = 0;
*(unsigned char *)packit = 'B';
}
/* IMAT <= 5: Non-unit triangular matrix */
if (*imat <= 5) {
zlatms_(n, n, dist, &iseed[1], type__, &rwork[1], &mode, &cndnum, &
anorm, &kl, &ku, packit, &ab_ref(ioff, 1), ldab, &work[1],
info);
/* IMAT > 5: Unit triangular matrix
The diagonal is deliberately set to something other than 1.
IMAT = 6: Matrix is the identity */
} else if (*imat == 6) {
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = 1, i__3 = *kd + 2 - j;
i__4 = *kd;
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
i__2 = ab_subscr(i__, j);
ab[i__2].r = 0., ab[i__2].i = 0.;
/* L10: */
}
i__4 = ab_subscr(*kd + 1, j);
ab[i__4].r = (doublereal) j, ab[i__4].i = 0.;
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__4 = ab_subscr(1, j);
ab[i__4].r = (doublereal) j, ab[i__4].i = 0.;
/* Computing MIN */
i__2 = *kd + 1, i__3 = *n - j + 1;
i__4 = min(i__2,i__3);
for (i__ = 2; i__ <= i__4; ++i__) {
i__2 = ab_subscr(i__, j);
ab[i__2].r = 0., ab[i__2].i = 0.;
/* L30: */
}
/* L40: */
}
}
/* IMAT > 6: Non-trivial unit triangular matrix
A unit triangular matrix T with condition CNDNUM is formed.
In this version, T only has bandwidth 2, the rest of it is zero. */
} else if (*imat <= 9) {
tnorm = sqrt(cndnum);
/* Initialize AB to zero. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__4 = 1, i__2 = *kd + 2 - j;
i__3 = *kd;
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
i__4 = ab_subscr(i__, j);
ab[i__4].r = 0., ab[i__4].i = 0.;
/* L50: */
}
i__3 = ab_subscr(*kd + 1, j);
d__1 = (doublereal) j;
ab[i__3].r = d__1, ab[i__3].i = 0.;
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__4 = *kd + 1, i__2 = *n - j + 1;
i__3 = min(i__4,i__2);
for (i__ = 2; i__ <= i__3; ++i__) {
i__4 = ab_subscr(i__, j);
ab[i__4].r = 0., ab[i__4].i = 0.;
/* L70: */
}
i__3 = ab_subscr(1, j);
d__1 = (doublereal) j;
ab[i__3].r = d__1, ab[i__3].i = 0.;
/* L80: */
}
}
/* Special case: T is tridiagonal. Set every other offdiagonal
so that the matrix has norm TNORM+1. */
if (*kd == 1) {
if (upper) {
i__1 = ab_subscr(1, 2);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = tnorm * z__2.r, z__1.i = tnorm * z__2.i;
ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
lenj = (*n - 3) / 2;
zlarnv_(&c__2, &iseed[1], &lenj, &work[1]);
i__1 = lenj;
for (j = 1; j <= i__1; ++j) {
i__3 = ab_subscr(1, j + 1 << 1);
i__4 = j;
z__1.r = tnorm * work[i__4].r, z__1.i = tnorm * work[i__4]
.i;
ab[i__3].r = z__1.r, ab[i__3].i = z__1.i;
/* L90: */
}
} else {
i__1 = ab_subscr(2, 1);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = tnorm * z__2.r, z__1.i = tnorm * z__2.i;
ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
lenj = (*n - 3) / 2;
zlarnv_(&c__2, &iseed[1], &lenj, &work[1]);
i__1 = lenj;
for (j = 1; j <= i__1; ++j) {
i__3 = ab_subscr(2, (j << 1) + 1);
i__4 = j;
z__1.r = tnorm * work[i__4].r, z__1.i = tnorm * work[i__4]
.i;
ab[i__3].r = z__1.r, ab[i__3].i = z__1.i;
/* L100: */
}
}
} else if (*kd > 1) {
/* Form a unit triangular matrix T with condition CNDNUM. T is
given by
| 1 + * |
| 1 + |
T = | 1 + * |
| 1 + |
| 1 + * |
| 1 + |
| . . . |
Each element marked with a '*' is formed by taking the product
of the adjacent elements marked with '+'. The '*'s can be
chosen freely, and the '+'s are chosen so that the inverse of
T will have elements of the same magnitude as T.
The two offdiagonals of T are stored in WORK. */
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = tnorm * z__2.r, z__1.i = tnorm * z__2.i;
star1.r = z__1.r, star1.i = z__1.i;
sfac = sqrt(tnorm);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = sfac * z__2.r, z__1.i = sfac * z__2.i;
plus1.r = z__1.r, plus1.i = z__1.i;
i__1 = *n;
for (j = 1; j <= i__1; j += 2) {
z_div(&z__1, &star1, &plus1);
plus2.r = z__1.r, plus2.i = z__1.i;
i__3 = j;
work[i__3].r = plus1.r, work[i__3].i = plus1.i;
i__3 = *n + j;
work[i__3].r = star1.r, work[i__3].i = star1.i;
if (j + 1 <= *n) {
i__3 = j + 1;
work[i__3].r = plus2.r, work[i__3].i = plus2.i;
i__3 = *n + j + 1;
work[i__3].r = 0., work[i__3].i = 0.;
z_div(&z__1, &star1, &plus2);
plus1.r = z__1.r, plus1.i = z__1.i;
/* Generate a new *-value with norm between sqrt(TNORM)
and TNORM. */
rexp = dlarnd_(&c__2, &iseed[1]);
if (rexp < 0.) {
d__2 = 1. - rexp;
d__1 = -pow_dd(&sfac, &d__2);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = d__1 * z__2.r, z__1.i = d__1 * z__2.i;
star1.r = z__1.r, star1.i = z__1.i;
} else {
d__2 = rexp + 1.;
d__1 = pow_dd(&sfac, &d__2);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = d__1 * z__2.r, z__1.i = d__1 * z__2.i;
star1.r = z__1.r, star1.i = z__1.i;
}
}
/* L110: */
}
/* Copy the tridiagonal T to AB. */
if (upper) {
i__1 = *n - 1;
zcopy_(&i__1, &work[1], &c__1, &ab_ref(*kd, 2), ldab);
i__1 = *n - 2;
zcopy_(&i__1, &work[*n + 1], &c__1, &ab_ref(*kd - 1, 3), ldab)
;
} else {
i__1 = *n - 1;
zcopy_(&i__1, &work[1], &c__1, &ab_ref(2, 1), ldab);
i__1 = *n - 2;
zcopy_(&i__1, &work[*n + 1], &c__1, &ab_ref(3, 1), ldab);
}
}
/* IMAT > 9: Pathological test cases. These triangular matrices
are badly scaled or badly conditioned, so when used in solving a
triangular system they may cause overflow in the solution vector. */
} else if (*imat == 10) {
/* Type 10: Generate a triangular matrix with elements between
-1 and 1. Give the diagonal norm 2 to make it well-conditioned.
Make the right hand side large so that it requires scaling. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = j - 1;
lenj = min(i__3,*kd);
zlarnv_(&c__4, &iseed[1], &lenj, &ab_ref(*kd + 1 - lenj, j));
i__3 = ab_subscr(*kd + 1, j);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r * 2., z__1.i = z__2.i * 2.;
ab[i__3].r = z__1.r, ab[i__3].i = z__1.i;
/* L120: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *n - j;
lenj = min(i__3,*kd);
if (lenj > 0) {
zlarnv_(&c__4, &iseed[1], &lenj, &ab_ref(2, j));
}
i__3 = ab_subscr(1, j);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r * 2., z__1.i = z__2.i * 2.;
ab[i__3].r = z__1.r, ab[i__3].i = z__1.i;
/* L130: */
}
}
/* Set the right hand side so that the largest value is BIGNUM. */
zlarnv_(&c__2, &iseed[1], n, &b[1]);
iy = izamax_(n, &b[1], &c__1);
bnorm = z_abs(&b[iy]);
bscal = bignum / max(1.,bnorm);
zdscal_(n, &bscal, &b[1], &c__1);
} else if (*imat == 11) {
/* Type 11: Make the first diagonal element in the solve small to
cause immediate overflow when dividing by T(j,j).
In type 11, the offdiagonal elements are small (CNORM(j) < 1). */
zlarnv_(&c__2, &iseed[1], n, &b[1]);
tscal = 1. / (doublereal) (*kd + 1);
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = j - 1;
lenj = min(i__3,*kd);
if (lenj > 0) {
zlarnv_(&c__4, &iseed[1], &lenj, &ab_ref(*kd + 2 - lenj,
j));
zdscal_(&lenj, &tscal, &ab_ref(*kd + 2 - lenj, j), &c__1);
}
i__3 = ab_subscr(*kd + 1, j);
zlarnd_(&z__1, &c__5, &iseed[1]);
ab[i__3].r = z__1.r, ab[i__3].i = z__1.i;
/* L140: */
}
i__1 = ab_subscr(*kd + 1, *n);
i__3 = ab_subscr(*kd + 1, *n);
z__1.r = smlnum * ab[i__3].r, z__1.i = smlnum * ab[i__3].i;
ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *n - j;
lenj = min(i__3,*kd);
if (lenj > 0) {
zlarnv_(&c__4, &iseed[1], &lenj, &ab_ref(2, j));
zdscal_(&lenj, &tscal, &ab_ref(2, j), &c__1);
}
i__3 = ab_subscr(1, j);
zlarnd_(&z__1, &c__5, &iseed[1]);
ab[i__3].r = z__1.r, ab[i__3].i = z__1.i;
/* L150: */
}
i__1 = ab_subscr(1, 1);
i__3 = ab_subscr(1, 1);
z__1.r = smlnum * ab[i__3].r, z__1.i = smlnum * ab[i__3].i;
ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
}
} else if (*imat == 12) {
/* Type 12: Make the first diagonal element in the solve small to
cause immediate overflow when dividing by T(j,j).
In type 12, the offdiagonal elements are O(1) (CNORM(j) > 1). */
zlarnv_(&c__2, &iseed[1], n, &b[1]);
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = j - 1;
lenj = min(i__3,*kd);
if (lenj > 0) {
zlarnv_(&c__4, &iseed[1], &lenj, &ab_ref(*kd + 2 - lenj,
j));
}
i__3 = ab_subscr(*kd + 1, j);
zlarnd_(&z__1, &c__5, &iseed[1]);
ab[i__3].r = z__1.r, ab[i__3].i = z__1.i;
/* L160: */
}
i__1 = ab_subscr(*kd + 1, *n);
i__3 = ab_subscr(*kd + 1, *n);
z__1.r = smlnum * ab[i__3].r, z__1.i = smlnum * ab[i__3].i;
ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *n - j;
lenj = min(i__3,*kd);
if (lenj > 0) {
zlarnv_(&c__4, &iseed[1], &lenj, &ab_ref(2, j));
}
i__3 = ab_subscr(1, j);
zlarnd_(&z__1, &c__5, &iseed[1]);
ab[i__3].r = z__1.r, ab[i__3].i = z__1.i;
/* L170: */
}
i__1 = ab_subscr(1, 1);
i__3 = ab_subscr(1, 1);
z__1.r = smlnum * ab[i__3].r, z__1.i = smlnum * ab[i__3].i;
ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
}
} else if (*imat == 13) {
/* Type 13: T is diagonal with small numbers on the diagonal to
make the growth factor underflow, but a small right hand side
chosen so that the solution does not overflow. */
if (upper) {
jcount = 1;
for (j = *n; j >= 1; --j) {
/* Computing MAX */
i__1 = 1, i__3 = *kd + 1 - (j - 1);
i__4 = *kd;
for (i__ = max(i__1,i__3); i__ <= i__4; ++i__) {
i__1 = ab_subscr(i__, j);
ab[i__1].r = 0., ab[i__1].i = 0.;
/* L180: */
}
if (jcount <= 2) {
i__4 = ab_subscr(*kd + 1, j);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = smlnum * z__2.r, z__1.i = smlnum * z__2.i;
ab[i__4].r = z__1.r, ab[i__4].i = z__1.i;
} else {
i__4 = ab_subscr(*kd + 1, j);
zlarnd_(&z__1, &c__5, &iseed[1]);
ab[i__4].r = z__1.r, ab[i__4].i = z__1.i;
}
++jcount;
if (jcount > 4) {
jcount = 1;
}
/* L190: */
}
} else {
jcount = 1;
i__4 = *n;
for (j = 1; j <= i__4; ++j) {
/* Computing MIN */
i__3 = *n - j + 1, i__2 = *kd + 1;
i__1 = min(i__3,i__2);
for (i__ = 2; i__ <= i__1; ++i__) {
i__3 = ab_subscr(i__, j);
ab[i__3].r = 0., ab[i__3].i = 0.;
/* L200: */
}
if (jcount <= 2) {
i__1 = ab_subscr(1, j);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = smlnum * z__2.r, z__1.i = smlnum * z__2.i;
ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
} else {
i__1 = ab_subscr(1, j);
zlarnd_(&z__1, &c__5, &iseed[1]);
ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
}
++jcount;
if (jcount > 4) {
jcount = 1;
}
/* L210: */
}
}
/* Set the right hand side alternately zero and small. */
if (upper) {
b[1].r = 0., b[1].i = 0.;
for (i__ = *n; i__ >= 2; i__ += -2) {
i__4 = i__;
b[i__4].r = 0., b[i__4].i = 0.;
i__4 = i__ - 1;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = smlnum * z__2.r, z__1.i = smlnum * z__2.i;
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
/* L220: */
}
} else {
i__4 = *n;
b[i__4].r = 0., b[i__4].i = 0.;
i__4 = *n - 1;
for (i__ = 1; i__ <= i__4; i__ += 2) {
i__1 = i__;
b[i__1].r = 0., b[i__1].i = 0.;
i__1 = i__ + 1;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = smlnum * z__2.r, z__1.i = smlnum * z__2.i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
/* L230: */
}
}
} else if (*imat == 14) {
/* Type 14: Make the diagonal elements small to cause gradual
overflow when dividing by T(j,j). To control the amount of
scaling needed, the matrix is bidiagonal. */
texp = 1. / (doublereal) (*kd + 1);
tscal = pow_dd(&smlnum, &texp);
zlarnv_(&c__4, &iseed[1], n, &b[1]);
if (upper) {
i__4 = *n;
for (j = 1; j <= i__4; ++j) {
/* Computing MAX */
i__1 = 1, i__3 = *kd + 2 - j;
i__2 = *kd;
for (i__ = max(i__1,i__3); i__ <= i__2; ++i__) {
i__1 = ab_subscr(i__, j);
ab[i__1].r = 0., ab[i__1].i = 0.;
/* L240: */
}
if (j > 1 && *kd > 0) {
i__2 = ab_subscr(*kd, j);
ab[i__2].r = -1., ab[i__2].i = -1.;
}
i__2 = ab_subscr(*kd + 1, j);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = tscal * z__2.r, z__1.i = tscal * z__2.i;
ab[i__2].r = z__1.r, ab[i__2].i = z__1.i;
/* L250: */
}
i__4 = *n;
b[i__4].r = 1., b[i__4].i = 1.;
} else {
i__4 = *n;
for (j = 1; j <= i__4; ++j) {
/* Computing MIN */
i__1 = *n - j + 1, i__3 = *kd + 1;
i__2 = min(i__1,i__3);
for (i__ = 3; i__ <= i__2; ++i__) {
i__1 = ab_subscr(i__, j);
ab[i__1].r = 0., ab[i__1].i = 0.;
/* L260: */
}
if (j < *n && *kd > 0) {
i__2 = ab_subscr(2, j);
ab[i__2].r = -1., ab[i__2].i = -1.;
}
i__2 = ab_subscr(1, j);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = tscal * z__2.r, z__1.i = tscal * z__2.i;
ab[i__2].r = z__1.r, ab[i__2].i = z__1.i;
/* L270: */
}
b[1].r = 1., b[1].i = 1.;
}
} else if (*imat == 15) {
/* Type 15: One zero diagonal element. */
iy = *n / 2 + 1;
if (upper) {
i__4 = *n;
for (j = 1; j <= i__4; ++j) {
/* Computing MIN */
i__2 = j, i__1 = *kd + 1;
lenj = min(i__2,i__1);
zlarnv_(&c__4, &iseed[1], &lenj, &ab_ref(*kd + 2 - lenj, j));
if (j != iy) {
i__2 = ab_subscr(*kd + 1, j);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r * 2., z__1.i = z__2.i * 2.;
ab[i__2].r = z__1.r, ab[i__2].i = z__1.i;
} else {
i__2 = ab_subscr(*kd + 1, j);
ab[i__2].r = 0., ab[i__2].i = 0.;
}
/* L280: */
}
} else {
i__4 = *n;
for (j = 1; j <= i__4; ++j) {
/* Computing MIN */
i__2 = *n - j + 1, i__1 = *kd + 1;
lenj = min(i__2,i__1);
zlarnv_(&c__4, &iseed[1], &lenj, &ab_ref(1, j));
if (j != iy) {
i__2 = ab_subscr(1, j);
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r * 2., z__1.i = z__2.i * 2.;
ab[i__2].r = z__1.r, ab[i__2].i = z__1.i;
} else {
i__2 = ab_subscr(1, j);
ab[i__2].r = 0., ab[i__2].i = 0.;
}
/* L290: */
}
}
zlarnv_(&c__2, &iseed[1], n, &b[1]);
zdscal_(n, &c_b91, &b[1], &c__1);
} else if (*imat == 16) {
/* Type 16: Make the offdiagonal elements large to cause overflow
when adding a column of T. In the non-transposed case, the
matrix is constructed to cause overflow when adding a column in
every other step. */
tscal = unfl / ulp;
tscal = (1. - ulp) / tscal;
i__4 = *n;
for (j = 1; j <= i__4; ++j) {
i__2 = *kd + 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__1 = ab_subscr(i__, j);
ab[i__1].r = 0., ab[i__1].i = 0.;
/* L300: */
}
/* L310: */
}
texp = 1.;
if (*kd > 0) {
if (upper) {
i__4 = -(*kd);
for (j = *n; i__4 < 0 ? j >= 1 : j <= 1; j += i__4) {
/* Computing MAX */
i__1 = 1, i__3 = j - *kd + 1;
i__2 = max(i__1,i__3);
for (i__ = j; i__ >= i__2; i__ += -2) {
i__1 = ab_subscr(j - i__ + 1, i__);
d__1 = -tscal / (doublereal) (*kd + 2);
ab[i__1].r = d__1, ab[i__1].i = 0.;
i__1 = ab_subscr(*kd + 1, i__);
ab[i__1].r = 1., ab[i__1].i = 0.;
i__1 = i__;
d__1 = texp * (1. - ulp);
b[i__1].r = d__1, b[i__1].i = 0.;
/* Computing MAX */
i__1 = 1, i__3 = j - *kd + 1;
if (i__ > max(i__1,i__3)) {
i__1 = ab_subscr(j - i__ + 2, i__ - 1);
d__1 = -(tscal / (doublereal) (*kd + 2)) / (
doublereal) (*kd + 3);
ab[i__1].r = d__1, ab[i__1].i = 0.;
i__1 = ab_subscr(*kd + 1, i__ - 1);
ab[i__1].r = 1., ab[i__1].i = 0.;
i__1 = i__ - 1;
d__1 = texp * (doublereal) ((*kd + 1) * (*kd + 1)
+ *kd);
b[i__1].r = d__1, b[i__1].i = 0.;
}
texp *= 2.;
/* L320: */
}
/* Computing MAX */
i__1 = 1, i__3 = j - *kd + 1;
i__2 = max(i__1,i__3);
d__1 = (doublereal) (*kd + 2) / (doublereal) (*kd + 3) *
tscal;
b[i__2].r = d__1, b[i__2].i = 0.;
/* L330: */
}
} else {
i__4 = *n;
i__2 = *kd;
for (j = 1; i__2 < 0 ? j >= i__4 : j <= i__4; j += i__2) {
texp = 1.;
/* Computing MIN */
i__1 = *kd + 1, i__3 = *n - j + 1;
lenj = min(i__1,i__3);
/* Computing MIN */
i__3 = *n, i__5 = j + *kd - 1;
i__1 = min(i__3,i__5);
for (i__ = j; i__ <= i__1; i__ += 2) {
i__3 = ab_subscr(lenj - (i__ - j), j);
d__1 = -tscal / (doublereal) (*kd + 2);
ab[i__3].r = d__1, ab[i__3].i = 0.;
i__3 = ab_subscr(1, j);
ab[i__3].r = 1., ab[i__3].i = 0.;
i__3 = j;
d__1 = texp * (1. - ulp);
b[i__3].r = d__1, b[i__3].i = 0.;
/* Computing MIN */
i__3 = *n, i__5 = j + *kd - 1;
if (i__ < min(i__3,i__5)) {
i__3 = ab_subscr(lenj - (i__ - j + 1), i__ + 1);
d__1 = -(tscal / (doublereal) (*kd + 2)) / (
doublereal) (*kd + 3);
ab[i__3].r = d__1, ab[i__3].i = 0.;
i__3 = ab_subscr(1, i__ + 1);
ab[i__3].r = 1., ab[i__3].i = 0.;
i__3 = i__ + 1;
d__1 = texp * (doublereal) ((*kd + 1) * (*kd + 1)
+ *kd);
b[i__3].r = d__1, b[i__3].i = 0.;
}
texp *= 2.;
/* L340: */
}
/* Computing MIN */
i__3 = *n, i__5 = j + *kd - 1;
i__1 = min(i__3,i__5);
d__1 = (doublereal) (*kd + 2) / (doublereal) (*kd + 3) *
tscal;
b[i__1].r = d__1, b[i__1].i = 0.;
/* L350: */
}
}
}
} else if (*imat == 17) {
/* Type 17: Generate a unit triangular matrix with elements
between -1 and 1, and make the right hand side large so that it
requires scaling. */
if (upper) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
/* Computing MIN */
i__4 = j - 1;
lenj = min(i__4,*kd);
zlarnv_(&c__4, &iseed[1], &lenj, &ab_ref(*kd + 1 - lenj, j));
i__4 = ab_subscr(*kd + 1, j);
d__1 = (doublereal) j;
ab[i__4].r = d__1, ab[i__4].i = 0.;
/* L360: */
}
} else {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
/* Computing MIN */
i__4 = *n - j;
lenj = min(i__4,*kd);
if (lenj > 0) {
zlarnv_(&c__4, &iseed[1], &lenj, &ab_ref(2, j));
}
i__4 = ab_subscr(1, j);
d__1 = (doublereal) j;
ab[i__4].r = d__1, ab[i__4].i = 0.;
/* L370: */
}
}
/* Set the right hand side so that the largest value is BIGNUM. */
zlarnv_(&c__2, &iseed[1], n, &b[1]);
iy = izamax_(n, &b[1], &c__1);
bnorm = z_abs(&b[iy]);
bscal = bignum / max(1.,bnorm);
zdscal_(n, &bscal, &b[1], &c__1);
} else if (*imat == 18) {
/* Type 18: Generate a triangular matrix with elements between
BIGNUM/(KD+1) and BIGNUM so that at least one of the column
norms will exceed BIGNUM.
1/3/91: ZLATBS no longer can handle this case */
tleft = bignum / (doublereal) (*kd + 1);
tscal = bignum * ((doublereal) (*kd + 1) / (doublereal) (*kd + 2));
if (upper) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
/* Computing MIN */
i__4 = j, i__1 = *kd + 1;
lenj = min(i__4,i__1);
zlarnv_(&c__5, &iseed[1], &lenj, &ab_ref(*kd + 2 - lenj, j));
dlarnv_(&c__1, &iseed[1], &lenj, &rwork[*kd + 2 - lenj]);
i__4 = *kd + 1;
for (i__ = *kd + 2 - lenj; i__ <= i__4; ++i__) {
i__1 = ab_subscr(i__, j);
i__3 = ab_subscr(i__, j);
d__1 = tleft + rwork[i__] * tscal;
z__1.r = d__1 * ab[i__3].r, z__1.i = d__1 * ab[i__3].i;
ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
/* L380: */
}
/* L390: */
}
} else {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
/* Computing MIN */
i__4 = *n - j + 1, i__1 = *kd + 1;
lenj = min(i__4,i__1);
zlarnv_(&c__5, &iseed[1], &lenj, &ab_ref(1, j));
dlarnv_(&c__1, &iseed[1], &lenj, &rwork[1]);
i__4 = lenj;
for (i__ = 1; i__ <= i__4; ++i__) {
i__1 = ab_subscr(i__, j);
i__3 = ab_subscr(i__, j);
d__1 = tleft + rwork[i__] * tscal;
z__1.r = d__1 * ab[i__3].r, z__1.i = d__1 * ab[i__3].i;
ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
/* L400: */
}
/* L410: */
}
}
zlarnv_(&c__2, &iseed[1], n, &b[1]);
zdscal_(n, &c_b91, &b[1], &c__1);
}
/* Flip the matrix if the transpose will be used. */
if (! lsame_(trans, "N")) {
if (upper) {
i__2 = *n / 2;
for (j = 1; j <= i__2; ++j) {
/* Computing MIN */
i__4 = *n - (j << 1) + 1, i__1 = *kd + 1;
lenj = min(i__4,i__1);
i__4 = *ldab - 1;
zswap_(&lenj, &ab_ref(*kd + 1, j), &i__4, &ab_ref(*kd + 2 -
lenj, *n - j + 1), &c_n1);
/* L420: */
}
} else {
i__2 = *n / 2;
for (j = 1; j <= i__2; ++j) {
/* Computing MIN */
i__4 = *n - (j << 1) + 1, i__1 = *kd + 1;
lenj = min(i__4,i__1);
i__4 = -(*ldab) + 1;
zswap_(&lenj, &ab_ref(1, j), &c__1, &ab_ref(lenj, *n - j + 2
- lenj), &i__4);
/* L430: */
}
}
}
return 0;
/* End of ZLATTB */
} /* zlattb_ */
/* Subroutine */ int zlatsp_(char *uplo, integer *n, doublecomplex *x,
integer *iseed)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublecomplex z__1, z__2, z__3;
/* Builtin functions */
double sqrt(doublereal), z_abs(doublecomplex *);
/* Local variables */
doublecomplex a, b, c__;
integer j;
doublecomplex r__;
integer n5, jj;
doublereal beta, alpha, alpha3;
extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *,
integer *);
/* -- LAPACK auxiliary test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLATSP generates a special test matrix for the complex symmetric */
/* (indefinite) factorization for packed matrices. The pivot blocks of */
/* the generated matrix will be in the following order: */
/* 2x2 pivot block, non diagonalizable */
/* 1x1 pivot block */
/* 2x2 pivot block, diagonalizable */
/* (cycle repeats) */
/* A row interchange is required for each non-diagonalizable 2x2 block. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER */
/* Specifies whether the generated matrix is to be upper or */
/* lower triangular. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* N (input) INTEGER */
/* The dimension of the matrix to be generated. */
/* X (output) COMPLEX*16 array, dimension (N*(N+1)/2) */
/* The generated matrix in packed storage format. The matrix */
/* consists of 3x3 and 2x2 diagonal blocks which result in the */
/* pivot sequence given above. The matrix outside these */
/* diagonal blocks is zero. */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry, the seed for the random number generator. The last */
/* of the four integers must be odd. (modified on exit) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants */
/* Parameter adjustments */
--iseed;
--x;
/* Function Body */
alpha = (sqrt(17.) + 1.) / 8.;
beta = alpha - .001;
alpha3 = alpha * alpha * alpha;
/* Fill the matrix with zeros. */
i__1 = *n * (*n + 1) / 2;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
x[i__2].r = 0., x[i__2].i = 0.;
/* L10: */
}
/* UPLO = 'U': Upper triangular storage */
if (*(unsigned char *)uplo == 'U') {
n5 = *n / 5;
n5 = *n - n5 * 5 + 1;
jj = *n * (*n + 1) / 2;
i__1 = n5;
for (j = *n; j >= i__1; j += -5) {
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = alpha3 * z__2.r, z__1.i = alpha3 * z__2.i;
a.r = z__1.r, a.i = z__1.i;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r / alpha, z__1.i = z__2.i / alpha;
b.r = z__1.r, b.i = z__1.i;
z__3.r = b.r * 2., z__3.i = b.i * 2.;
z__2.r = z__3.r * 0. - z__3.i * 1., z__2.i = z__3.r * 1. + z__3.i
* 0.;
z__1.r = a.r - z__2.r, z__1.i = a.i - z__2.i;
c__.r = z__1.r, c__.i = z__1.i;
z__1.r = c__.r / beta, z__1.i = c__.i / beta;
r__.r = z__1.r, r__.i = z__1.i;
i__2 = jj;
x[i__2].r = a.r, x[i__2].i = a.i;
i__2 = jj - 2;
x[i__2].r = b.r, x[i__2].i = b.i;
jj -= j;
i__2 = jj;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
i__2 = jj - 1;
x[i__2].r = r__.r, x[i__2].i = r__.i;
jj -= j - 1;
i__2 = jj;
x[i__2].r = c__.r, x[i__2].i = c__.i;
jj -= j - 2;
i__2 = jj;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
jj -= j - 3;
i__2 = jj;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
if (z_abs(&x[jj + (j - 3)]) > z_abs(&x[jj])) {
i__2 = jj + (j - 4);
i__3 = jj + (j - 3);
z__1.r = x[i__3].r * 2., z__1.i = x[i__3].i * 2.;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
} else {
i__2 = jj + (j - 4);
i__3 = jj;
z__1.r = x[i__3].r * 2., z__1.i = x[i__3].i * 2.;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
}
jj -= j - 4;
/* L20: */
}
/* Clean-up for N not a multiple of 5. */
j = n5 - 1;
if (j > 2) {
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = alpha3 * z__2.r, z__1.i = alpha3 * z__2.i;
a.r = z__1.r, a.i = z__1.i;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r / alpha, z__1.i = z__2.i / alpha;
b.r = z__1.r, b.i = z__1.i;
z__3.r = b.r * 2., z__3.i = b.i * 2.;
z__2.r = z__3.r * 0. - z__3.i * 1., z__2.i = z__3.r * 1. + z__3.i
* 0.;
z__1.r = a.r - z__2.r, z__1.i = a.i - z__2.i;
c__.r = z__1.r, c__.i = z__1.i;
z__1.r = c__.r / beta, z__1.i = c__.i / beta;
r__.r = z__1.r, r__.i = z__1.i;
i__1 = jj;
x[i__1].r = a.r, x[i__1].i = a.i;
i__1 = jj - 2;
x[i__1].r = b.r, x[i__1].i = b.i;
jj -= j;
i__1 = jj;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
i__1 = jj - 1;
x[i__1].r = r__.r, x[i__1].i = r__.i;
jj -= j - 1;
i__1 = jj;
x[i__1].r = c__.r, x[i__1].i = c__.i;
jj -= j - 2;
j += -3;
}
if (j > 1) {
i__1 = jj;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
i__1 = jj - j;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
if (z_abs(&x[jj]) > z_abs(&x[jj - j])) {
i__1 = jj - 1;
i__2 = jj;
z__1.r = x[i__2].r * 2., z__1.i = x[i__2].i * 2.;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
} else {
i__1 = jj - 1;
i__2 = jj - j;
z__1.r = x[i__2].r * 2., z__1.i = x[i__2].i * 2.;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
}
jj = jj - j - (j - 1);
j += -2;
} else if (j == 1) {
i__1 = jj;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
--j;
}
/* UPLO = 'L': Lower triangular storage */
} else {
n5 = *n / 5;
n5 *= 5;
jj = 1;
i__1 = n5;
for (j = 1; j <= i__1; j += 5) {
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = alpha3 * z__2.r, z__1.i = alpha3 * z__2.i;
a.r = z__1.r, a.i = z__1.i;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r / alpha, z__1.i = z__2.i / alpha;
b.r = z__1.r, b.i = z__1.i;
z__3.r = b.r * 2., z__3.i = b.i * 2.;
z__2.r = z__3.r * 0. - z__3.i * 1., z__2.i = z__3.r * 1. + z__3.i
* 0.;
z__1.r = a.r - z__2.r, z__1.i = a.i - z__2.i;
c__.r = z__1.r, c__.i = z__1.i;
z__1.r = c__.r / beta, z__1.i = c__.i / beta;
r__.r = z__1.r, r__.i = z__1.i;
i__2 = jj;
x[i__2].r = a.r, x[i__2].i = a.i;
i__2 = jj + 2;
x[i__2].r = b.r, x[i__2].i = b.i;
jj += *n - j + 1;
i__2 = jj;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
i__2 = jj + 1;
x[i__2].r = r__.r, x[i__2].i = r__.i;
jj += *n - j;
i__2 = jj;
x[i__2].r = c__.r, x[i__2].i = c__.i;
jj += *n - j - 1;
i__2 = jj;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
jj += *n - j - 2;
i__2 = jj;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
if (z_abs(&x[jj - (*n - j - 2)]) > z_abs(&x[jj])) {
i__2 = jj - (*n - j - 2) + 1;
i__3 = jj - (*n - j - 2);
z__1.r = x[i__3].r * 2., z__1.i = x[i__3].i * 2.;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
} else {
i__2 = jj - (*n - j - 2) + 1;
i__3 = jj;
z__1.r = x[i__3].r * 2., z__1.i = x[i__3].i * 2.;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
}
jj += *n - j - 3;
/* L30: */
}
/* Clean-up for N not a multiple of 5. */
j = n5 + 1;
if (j < *n - 1) {
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = alpha3 * z__2.r, z__1.i = alpha3 * z__2.i;
a.r = z__1.r, a.i = z__1.i;
zlarnd_(&z__2, &c__5, &iseed[1]);
z__1.r = z__2.r / alpha, z__1.i = z__2.i / alpha;
b.r = z__1.r, b.i = z__1.i;
z__3.r = b.r * 2., z__3.i = b.i * 2.;
z__2.r = z__3.r * 0. - z__3.i * 1., z__2.i = z__3.r * 1. + z__3.i
* 0.;
z__1.r = a.r - z__2.r, z__1.i = a.i - z__2.i;
c__.r = z__1.r, c__.i = z__1.i;
z__1.r = c__.r / beta, z__1.i = c__.i / beta;
r__.r = z__1.r, r__.i = z__1.i;
i__1 = jj;
x[i__1].r = a.r, x[i__1].i = a.i;
i__1 = jj + 2;
x[i__1].r = b.r, x[i__1].i = b.i;
jj += *n - j + 1;
i__1 = jj;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
i__1 = jj + 1;
x[i__1].r = r__.r, x[i__1].i = r__.i;
jj += *n - j;
i__1 = jj;
x[i__1].r = c__.r, x[i__1].i = c__.i;
jj += *n - j - 1;
j += 3;
}
if (j < *n) {
i__1 = jj;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
i__1 = jj + (*n - j + 1);
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
if (z_abs(&x[jj]) > z_abs(&x[jj + (*n - j + 1)])) {
i__1 = jj + 1;
i__2 = jj;
z__1.r = x[i__2].r * 2., z__1.i = x[i__2].i * 2.;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
} else {
i__1 = jj + 1;
i__2 = jj + (*n - j + 1);
z__1.r = x[i__2].r * 2., z__1.i = x[i__2].i * 2.;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
}
jj = jj + (*n - j + 1) + (*n - j);
j += 2;
} else if (j == *n) {
i__1 = jj;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
jj += *n - j + 1;
++j;
}
}
return 0;
/* End of ZLATSP */
} /* zlatsp_ */
/* Subroutine */ int zckglm_(integer *nn, integer *nval, integer *mval,
integer *pval, integer *nmats, integer *iseed, doublereal *thresh,
integer *nmax, doublecomplex *a, doublecomplex *af, doublecomplex *b,
doublecomplex *bf, doublecomplex *x, doublecomplex *work, doublereal *
rwork, integer *nin, integer *nout, integer *info)
{
/* Format strings */
static char fmt_9997[] = "(\002 *** Invalid input for GLM: M = \002,"
"i6,\002, P = \002,i6,\002, N = \002,i6,\002;\002,/\002 must "
"satisfy M <= N <= M+P \002,\002(this set of values will be skip"
"ped)\002)";
static char fmt_9999[] = "(\002 ZLATMS in ZCKGLM INFO = \002,i5)";
static char fmt_9998[] = "(\002 N=\002,i4,\002 M=\002,i4,\002, P=\002,"
"i4,\002, type \002,i2,\002, test \002,i2,\002, ratio=\002,g13.6)";
/* System generated locals */
integer i__1, i__2, i__3;
doublecomplex z__1;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsle(cilist *), e_wsle(void), s_wsfe(cilist *), do_fio(integer *
, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, m, n, p, ik, lda, ldb, kla, klb, kua, kub, imat;
char path[3], type__[1];
integer nrun, modea, modeb, nfail;
char dista[1], distb[1];
integer iinfo;
doublereal resid, anorm, bnorm;
integer lwork;
extern /* Subroutine */ int dlatb9_(char *, integer *, integer *, integer
*, integer *, char *, integer *, integer *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
doublereal *, char *, char *),
alahdg_(integer *, char *);
doublereal cndnma, cndnmb;
extern /* Subroutine */ int alareq_(char *, integer *, logical *, integer
*, integer *, integer *), alasum_(char *, integer *,
integer *, integer *, integer *);
extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *,
integer *);
logical dotype[8];
extern /* Subroutine */ int zlatms_(integer *, integer *, char *, integer
*, char *, doublereal *, integer *, doublereal *, doublereal *,
integer *, integer *, char *, doublecomplex *, integer *,
doublecomplex *, integer *);
logical firstt;
extern /* Subroutine */ int zglmts_(integer *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublereal *, doublereal *);
/* Fortran I/O blocks */
static cilist io___13 = { 0, 0, 0, 0, 0 };
static cilist io___14 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___30 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___31 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___34 = { 0, 0, 0, fmt_9998, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZCKGLM tests ZGGGLM - subroutine for solving generalized linear */
/* model problem. */
/* Arguments */
/* ========= */
/* NN (input) INTEGER */
/* The number of values of N, M and P contained in the vectors */
/* NVAL, MVAL and PVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix row dimension N. */
/* MVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix column dimension M. */
/* PVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix column dimension P. */
/* NMATS (input) INTEGER */
/* The number of matrix types to be tested for each combination */
/* of matrix dimensions. If NMATS >= NTYPES (the maximum */
/* number of matrix types), then all the different types are */
/* generated for testing. If NMATS < NTYPES, another input line */
/* is read to get the numbers of the matrix types to be used. */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry, the seed of the random number generator. The array */
/* elements should be between 0 and 4095, otherwise they will be */
/* reduced mod 4096, and ISEED(4) must be odd. */
/* On exit, the next seed in the random number sequence after */
/* all the test matrices have been generated. */
/* THRESH (input) DOUBLE PRECISION */
/* The threshold value for the test ratios. A result is */
/* included in the output file if RESID >= THRESH. To have */
/* every test ratio printed, use THRESH = 0. */
/* NMAX (input) INTEGER */
/* The maximum value permitted for M or N, used in dimensioning */
/* the work arrays. */
/* A (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* AF (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* B (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* BF (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* X (workspace) COMPLEX*16 array, dimension (4*NMAX) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (NMAX) */
/* WORK (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* NIN (input) INTEGER */
/* The unit number for input. */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* INFO (output) INTEGER */
/* = 0 : successful exit */
/* > 0 : If ZLATMS returns an error code, the absolute value */
/* of it is returned. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants. */
/* Parameter adjustments */
--rwork;
--work;
--x;
--bf;
--b;
--af;
--a;
--iseed;
--pval;
--mval;
--nval;
/* Function Body */
s_copy(path, "GLM", (ftnlen)3, (ftnlen)3);
*info = 0;
nrun = 0;
nfail = 0;
firstt = TRUE_;
alareq_(path, nmats, dotype, &c__8, nin, nout);
lda = *nmax;
ldb = *nmax;
lwork = *nmax * *nmax;
/* Check for valid input values. */
i__1 = *nn;
for (ik = 1; ik <= i__1; ++ik) {
m = mval[ik];
p = pval[ik];
n = nval[ik];
if (m > n || n > m + p) {
if (firstt) {
io___13.ciunit = *nout;
s_wsle(&io___13);
e_wsle();
firstt = FALSE_;
}
io___14.ciunit = *nout;
s_wsfe(&io___14);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&p, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
e_wsfe();
}
/* L10: */
}
firstt = TRUE_;
/* Do for each value of M in MVAL. */
i__1 = *nn;
for (ik = 1; ik <= i__1; ++ik) {
m = mval[ik];
p = pval[ik];
n = nval[ik];
if (m > n || n > m + p) {
goto L40;
}
for (imat = 1; imat <= 8; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat - 1]) {
goto L30;
}
/* Set up parameters with DLATB9 and generate test */
/* matrices A and B with ZLATMS. */
dlatb9_(path, &imat, &m, &p, &n, type__, &kla, &kua, &klb, &kub, &
anorm, &bnorm, &modea, &modeb, &cndnma, &cndnmb, dista,
distb);
zlatms_(&n, &m, dista, &iseed[1], type__, &rwork[1], &modea, &
cndnma, &anorm, &kla, &kua, "No packing", &a[1], &lda, &
work[1], &iinfo);
if (iinfo != 0) {
io___30.ciunit = *nout;
s_wsfe(&io___30);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L30;
}
zlatms_(&n, &p, distb, &iseed[1], type__, &rwork[1], &modeb, &
cndnmb, &bnorm, &klb, &kub, "No packing", &b[1], &ldb, &
work[1], &iinfo);
if (iinfo != 0) {
io___31.ciunit = *nout;
s_wsfe(&io___31);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L30;
}
/* Generate random left hand side vector of GLM */
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
zlarnd_(&z__1, &c__2, &iseed[1]);
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
/* L20: */
}
zglmts_(&n, &m, &p, &a[1], &af[1], &lda, &b[1], &bf[1], &ldb, &x[
1], &x[*nmax + 1], &x[(*nmax << 1) + 1], &x[*nmax * 3 + 1]
, &work[1], &lwork, &rwork[1], &resid);
/* Print information about the tests that did not */
/* pass the threshold. */
if (resid >= *thresh) {
if (nfail == 0 && firstt) {
firstt = FALSE_;
alahdg_(nout, path);
}
io___34.ciunit = *nout;
s_wsfe(&io___34);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&p, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&c__1, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&resid, (ftnlen)sizeof(doublereal));
e_wsfe();
++nfail;
}
++nrun;
L30:
;
}
L40:
;
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &c__0);
return 0;
/* End of ZCKGLM */
} /* zckglm_ */
