/* Subroutine */ int zchkgb_(logical *dotype, integer *nm, integer *mval,
integer *nn, integer *nval, integer *nnb, integer *nbval, integer *
nns, integer *nsval, doublereal *thresh, logical *tsterr,
doublecomplex *a, integer *la, doublecomplex *afac, integer *lafac,
doublecomplex *b, doublecomplex *x, doublecomplex *xact,
doublecomplex *work, doublereal *rwork, integer *iwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char transs[1*3] = "N" "T" "C";
/* Format strings */
static char fmt_9999[] = "(\002 *** In ZCHKGB, LA=\002,i5,\002 is too sm"
"all for M=\002,i5,\002, N=\002,i5,\002, KL=\002,i4,\002, KU=\002"
",i4,/\002 ==> Increase LA to at least \002,i5)";
static char fmt_9998[] = "(\002 *** In ZCHKGB, LAFAC=\002,i5,\002 is too"
" small for M=\002,i5,\002, N=\002,i5,\002, KL=\002,i4,\002, KU"
"=\002,i4,/\002 ==> Increase LAFAC to at least \002,i5)";
static char fmt_9997[] = "(\002 M =\002,i5,\002, N =\002,i5,\002, KL="
"\002,i5,\002, KU=\002,i5,\002, NB =\002,i4,\002, type \002,i1"
",\002, test(\002,i1,\002)=\002,g12.5)";
static char fmt_9996[] = "(\002 TRANS='\002,a1,\002', N=\002,i5,\002, "
"KL=\002,i5,\002, KU=\002,i5,\002, NRHS=\002,i3,\002, type \002,i"
"1,\002, test(\002,i1,\002)=\002,g12.5)";
static char fmt_9995[] = "(\002 NORM ='\002,a1,\002', N=\002,i5,\002, "
"KL=\002,i5,\002, KU=\002,i5,\002,\002,10x,\002 type \002,i1,\002"
", test(\002,i1,\002)=\002,g12.5)";
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9, i__10,
i__11;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, j, k, m, n, i1, i2, nb, im, in, kl, ku, lda, ldb, inb, ikl,
nkl, iku, nku, ioff, mode, koff, imat, info;
char path[3], dist[1];
integer irhs, nrhs;
char norm[1], type__[1];
integer nrun;
extern /* Subroutine */ int alahd_(integer *, char *);
integer nfail, iseed[4];
extern doublereal dget06_(doublereal *, doublereal *);
doublereal rcond;
extern /* Subroutine */ int zgbt01_(integer *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
integer *, doublecomplex *, doublereal *);
integer nimat, klval[4];
extern /* Subroutine */ int zgbt02_(char *, integer *, integer *, integer
*, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *), zgbt05_(char *, integer *, integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *
, doublereal *, doublereal *, doublereal *);
doublereal anorm;
integer itran;
extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *
);
integer kuval[4];
char trans[1];
integer izero, nerrs;
logical zerot;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
char xtype[1];
extern /* Subroutine */ int zlatb4_(char *, integer *, integer *, integer
*, char *, integer *, integer *, doublereal *, integer *,
doublereal *, char *);
integer ldafac;
extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *,
char *, integer *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *, integer *);
doublereal rcondc;
extern doublereal zlangb_(char *, integer *, integer *, integer *,
doublecomplex *, integer *, doublereal *);
doublereal rcondi;
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer
*, integer *);
doublereal cndnum, anormi, rcondo;
extern /* Subroutine */ int zgbcon_(char *, integer *, integer *, integer
*, doublecomplex *, integer *, integer *, doublereal *,
doublereal *, doublecomplex *, doublereal *, integer *);
doublereal ainvnm;
logical trfcon;
doublereal anormo;
extern /* Subroutine */ int xlaenv_(integer *, integer *), zerrge_(char *,
integer *), zgbrfs_(char *, integer *, integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *
, integer *, doublereal *, doublereal *, doublecomplex *,
doublereal *, integer *), zgbtrf_(integer *, integer *,
integer *, integer *, doublecomplex *, integer *, integer *,
integer *), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *), zlarhs_(char *,
char *, char *, char *, integer *, integer *, integer *, integer *
, integer *, doublecomplex *, integer *, doublecomplex *, integer
*, doublecomplex *, integer *, integer *, integer *), zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *), zgbtrs_(char *, integer *, integer *, integer *, integer
*, doublecomplex *, integer *, integer *, doublecomplex *,
integer *, integer *), zlatms_(integer *, integer *, char
*, integer *, char *, doublereal *, integer *, doublereal *,
doublereal *, integer *, integer *, char *, doublecomplex *,
integer *, doublecomplex *, integer *);
doublereal result[7];
/* Fortran I/O blocks */
static cilist io___25 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___26 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___59 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___61 = { 0, 0, 0, fmt_9995, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZCHKGB tests ZGBTRF, -TRS, -RFS, and -CON */
/* Arguments */
/* ========= */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* The matrix types to be used for testing. Matrices of type j */
/* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */
/* NM (input) INTEGER */
/* The number of values of M contained in the vector MVAL. */
/* MVAL (input) INTEGER array, dimension (NM) */
/* The values of the matrix row dimension M. */
/* 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 column dimension N. */
/* NNB (input) INTEGER */
/* The number of values of NB contained in the vector NBVAL. */
/* NBVAL (input) INTEGER array, dimension (NBVAL) */
/* The values of the blocksize NB. */
/* NNS (input) INTEGER */
/* The number of values of NRHS contained in the vector NSVAL. */
/* NSVAL (input) INTEGER array, dimension (NNS) */
/* The values of the number of right hand sides NRHS. */
/* 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. */
/* TSTERR (input) LOGICAL */
/* Flag that indicates whether error exits are to be tested. */
/* A (workspace) COMPLEX*16 array, dimension (LA) */
/* LA (input) INTEGER */
/* The length of the array A. LA >= (KLMAX+KUMAX+1)*NMAX */
/* where KLMAX is the largest entry in the local array KLVAL, */
/* KUMAX is the largest entry in the local array KUVAL and */
/* NMAX is the largest entry in the input array NVAL. */
/* AFAC (workspace) COMPLEX*16 array, dimension (LAFAC) */
/* LAFAC (input) INTEGER */
/* The length of the array AFAC. LAFAC >= (2*KLMAX+KUMAX+1)*NMAX */
/* where KLMAX is the largest entry in the local array KLVAL, */
/* KUMAX is the largest entry in the local array KUVAL and */
/* NMAX is the largest entry in the input array NVAL. */
/* B (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* X (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* XACT (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* WORK (workspace) COMPLEX*16 array, dimension */
/* (NMAX*max(3,NSMAX,NMAX)) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension */
/* (max(NMAX,2*NSMAX)) */
/* IWORK (workspace) INTEGER array, dimension (NMAX) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--iwork;
--rwork;
--work;
--xact;
--x;
--b;
--afac;
--a;
--nsval;
--nbval;
--nval;
--mval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "GB", (ftnlen)2, (ftnlen)2);
nrun = 0;
nfail = 0;
nerrs = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
/* Test the error exits */
if (*tsterr) {
zerrge_(path, nout);
}
infoc_1.infot = 0;
/* Initialize the first value for the lower and upper bandwidths. */
klval[0] = 0;
kuval[0] = 0;
/* Do for each value of M in MVAL */
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
m = mval[im];
/* Set values to use for the lower bandwidth. */
klval[1] = m + (m + 1) / 4;
/* KLVAL( 2 ) = MAX( M-1, 0 ) */
klval[2] = (m * 3 - 1) / 4;
klval[3] = (m + 1) / 4;
/* Do for each value of N in NVAL */
i__2 = *nn;
for (in = 1; in <= i__2; ++in) {
n = nval[in];
*(unsigned char *)xtype = 'N';
/* Set values to use for the upper bandwidth. */
kuval[1] = n + (n + 1) / 4;
/* KUVAL( 2 ) = MAX( N-1, 0 ) */
kuval[2] = (n * 3 - 1) / 4;
kuval[3] = (n + 1) / 4;
/* Set limits on the number of loop iterations. */
/* Computing MIN */
i__3 = m + 1;
nkl = min(i__3,4);
if (n == 0) {
nkl = 2;
}
/* Computing MIN */
i__3 = n + 1;
nku = min(i__3,4);
if (m == 0) {
nku = 2;
}
nimat = 8;
if (m <= 0 || n <= 0) {
nimat = 1;
}
i__3 = nkl;
for (ikl = 1; ikl <= i__3; ++ikl) {
/* Do for KL = 0, (5*M+1)/4, (3M-1)/4, and (M+1)/4. This */
/* order makes it easier to skip redundant values for small */
/* values of M. */
kl = klval[ikl - 1];
i__4 = nku;
for (iku = 1; iku <= i__4; ++iku) {
/* Do for KU = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This */
/* order makes it easier to skip redundant values for */
/* small values of N. */
ku = kuval[iku - 1];
/* Check that A and AFAC are big enough to generate this */
/* matrix. */
lda = kl + ku + 1;
ldafac = (kl << 1) + ku + 1;
if (lda * n > *la || ldafac * n > *lafac) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
if (n * (kl + ku + 1) > *la) {
io___25.ciunit = *nout;
s_wsfe(&io___25);
do_fio(&c__1, (char *)&(*la), (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(integer)
);
i__5 = n * (kl + ku + 1);
do_fio(&c__1, (char *)&i__5, (ftnlen)sizeof(
integer));
e_wsfe();
++nerrs;
}
if (n * ((kl << 1) + ku + 1) > *lafac) {
io___26.ciunit = *nout;
s_wsfe(&io___26);
do_fio(&c__1, (char *)&(*lafac), (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(integer)
);
i__5 = n * ((kl << 1) + ku + 1);
do_fio(&c__1, (char *)&i__5, (ftnlen)sizeof(
integer));
e_wsfe();
++nerrs;
}
goto L130;
}
i__5 = nimat;
for (imat = 1; imat <= i__5; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L120;
}
/* Skip types 2, 3, or 4 if the matrix size is too */
/* small. */
zerot = imat >= 2 && imat <= 4;
if (zerot && n < imat - 1) {
goto L120;
}
if (! zerot || ! dotype[1]) {
/* Set up parameters with ZLATB4 and generate a */
/* test matrix with ZLATMS. */
zlatb4_(path, &imat, &m, &n, type__, &kl, &ku, &
anorm, &mode, &cndnum, dist);
/* Computing MAX */
i__6 = 1, i__7 = ku + 2 - n;
koff = max(i__6,i__7);
i__6 = koff - 1;
for (i__ = 1; i__ <= i__6; ++i__) {
i__7 = i__;
a[i__7].r = 0., a[i__7].i = 0.;
/* L20: */
}
s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)6, (
ftnlen)6);
zlatms_(&m, &n, dist, iseed, type__, &rwork[1], &
mode, &cndnum, &anorm, &kl, &ku, "Z", &a[
koff], &lda, &work[1], &info);
/* Check the error code from ZLATMS. */
if (info != 0) {
alaerh_(path, "ZLATMS", &info, &c__0, " ", &m,
&n, &kl, &ku, &c_n1, &imat, &nfail, &
nerrs, nout);
goto L120;
}
} else if (izero > 0) {
/* Use the same matrix for types 3 and 4 as for */
/* type 2 by copying back the zeroed out column. */
i__6 = i2 - i1 + 1;
zcopy_(&i__6, &b[1], &c__1, &a[ioff + i1], &c__1);
}
/* For types 2, 3, and 4, zero one or more columns of */
/* the matrix to test that INFO is returned correctly. */
izero = 0;
if (zerot) {
if (imat == 2) {
izero = 1;
} else if (imat == 3) {
izero = min(m,n);
} else {
izero = min(m,n) / 2 + 1;
}
ioff = (izero - 1) * lda;
if (imat < 4) {
/* Store the column to be zeroed out in B. */
/* Computing MAX */
i__6 = 1, i__7 = ku + 2 - izero;
i1 = max(i__6,i__7);
/* Computing MIN */
i__6 = kl + ku + 1, i__7 = ku + 1 + (m -
izero);
i2 = min(i__6,i__7);
i__6 = i2 - i1 + 1;
zcopy_(&i__6, &a[ioff + i1], &c__1, &b[1], &
c__1);
i__6 = i2;
for (i__ = i1; i__ <= i__6; ++i__) {
i__7 = ioff + i__;
a[i__7].r = 0., a[i__7].i = 0.;
/* L30: */
}
} else {
i__6 = n;
for (j = izero; j <= i__6; ++j) {
/* Computing MAX */
i__7 = 1, i__8 = ku + 2 - j;
/* Computing MIN */
i__10 = kl + ku + 1, i__11 = ku + 1 + (m
- j);
i__9 = min(i__10,i__11);
for (i__ = max(i__7,i__8); i__ <= i__9;
++i__) {
i__7 = ioff + i__;
a[i__7].r = 0., a[i__7].i = 0.;
/* L40: */
}
ioff += lda;
/* L50: */
}
}
}
/* These lines, if used in place of the calls in the */
/* loop over INB, cause the code to bomb on a Sun */
/* SPARCstation. */
/* ANORMO = ZLANGB( 'O', N, KL, KU, A, LDA, RWORK ) */
/* ANORMI = ZLANGB( 'I', N, KL, KU, A, LDA, RWORK ) */
/* Do for each blocksize in NBVAL */
i__6 = *nnb;
for (inb = 1; inb <= i__6; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
/* Compute the LU factorization of the band matrix. */
if (m > 0 && n > 0) {
i__9 = kl + ku + 1;
zlacpy_("Full", &i__9, &n, &a[1], &lda, &afac[
kl + 1], &ldafac);
}
s_copy(srnamc_1.srnamt, "ZGBTRF", (ftnlen)6, (
ftnlen)6);
zgbtrf_(&m, &n, &kl, &ku, &afac[1], &ldafac, &
iwork[1], &info);
/* Check error code from ZGBTRF. */
if (info != izero) {
alaerh_(path, "ZGBTRF", &info, &izero, " ", &
m, &n, &kl, &ku, &nb, &imat, &nfail, &
nerrs, nout);
}
trfcon = FALSE_;
/* + TEST 1 */
/* Reconstruct matrix from factors and compute */
/* residual. */
zgbt01_(&m, &n, &kl, &ku, &a[1], &lda, &afac[1], &
ldafac, &iwork[1], &work[1], result);
/* Print information about the tests so far that */
/* did not pass the threshold. */
if (result[0] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___45.ciunit = *nout;
s_wsfe(&io___45);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&nb, (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 *)&result[0], (ftnlen)
sizeof(doublereal));
e_wsfe();
++nfail;
}
++nrun;
/* Skip the remaining tests if this is not the */
/* first block size or if M .ne. N. */
if (inb > 1 || m != n) {
goto L110;
}
anormo = zlangb_("O", &n, &kl, &ku, &a[1], &lda, &
rwork[1]);
anormi = zlangb_("I", &n, &kl, &ku, &a[1], &lda, &
rwork[1]);
if (info == 0) {
/* Form the inverse of A so we can get a good */
/* estimate of CNDNUM = norm(A) * norm(inv(A)). */
ldb = max(1,n);
zlaset_("Full", &n, &n, &c_b61, &c_b62, &work[
1], &ldb);
s_copy(srnamc_1.srnamt, "ZGBTRS", (ftnlen)6, (
ftnlen)6);
zgbtrs_("No transpose", &n, &kl, &ku, &n, &
afac[1], &ldafac, &iwork[1], &work[1],
&ldb, &info);
/* Compute the 1-norm condition number of A. */
ainvnm = zlange_("O", &n, &n, &work[1], &ldb,
&rwork[1]);
if (anormo <= 0. || ainvnm <= 0.) {
rcondo = 1.;
} else {
rcondo = 1. / anormo / ainvnm;
}
/* Compute the infinity-norm condition number of */
/* A. */
ainvnm = zlange_("I", &n, &n, &work[1], &ldb,
&rwork[1]);
if (anormi <= 0. || ainvnm <= 0.) {
rcondi = 1.;
} else {
rcondi = 1. / anormi / ainvnm;
}
} else {
/* Do only the condition estimate if INFO.NE.0. */
trfcon = TRUE_;
rcondo = 0.;
rcondi = 0.;
}
/* Skip the solve tests if the matrix is singular. */
if (trfcon) {
goto L90;
}
i__9 = *nns;
for (irhs = 1; irhs <= i__9; ++irhs) {
nrhs = nsval[irhs];
*(unsigned char *)xtype = 'N';
for (itran = 1; itran <= 3; ++itran) {
*(unsigned char *)trans = *(unsigned char
*)&transs[itran - 1];
if (itran == 1) {
rcondc = rcondo;
*(unsigned char *)norm = 'O';
} else {
rcondc = rcondi;
*(unsigned char *)norm = 'I';
}
/* + TEST 2: */
/* Solve and compute residual for A * X = B. */
s_copy(srnamc_1.srnamt, "ZLARHS", (ftnlen)
6, (ftnlen)6);
zlarhs_(path, xtype, " ", trans, &n, &n, &
kl, &ku, &nrhs, &a[1], &lda, &
xact[1], &ldb, &b[1], &ldb, iseed,
&info);
*(unsigned char *)xtype = 'C';
zlacpy_("Full", &n, &nrhs, &b[1], &ldb, &
x[1], &ldb);
s_copy(srnamc_1.srnamt, "ZGBTRS", (ftnlen)
6, (ftnlen)6);
zgbtrs_(trans, &n, &kl, &ku, &nrhs, &afac[
1], &ldafac, &iwork[1], &x[1], &
ldb, &info);
/* Check error code from ZGBTRS. */
if (info != 0) {
alaerh_(path, "ZGBTRS", &info, &c__0,
trans, &n, &n, &kl, &ku, &
c_n1, &imat, &nfail, &nerrs,
nout);
}
zlacpy_("Full", &n, &nrhs, &b[1], &ldb, &
work[1], &ldb);
zgbt02_(trans, &m, &n, &kl, &ku, &nrhs, &
a[1], &lda, &x[1], &ldb, &work[1],
&ldb, &result[1]);
/* + TEST 3: */
/* Check solution from generated exact */
/* solution. */
zget04_(&n, &nrhs, &x[1], &ldb, &xact[1],
&ldb, &rcondc, &result[2]);
/* + TESTS 4, 5, 6: */
/* Use iterative refinement to improve the */
/* solution. */
s_copy(srnamc_1.srnamt, "ZGBRFS", (ftnlen)
6, (ftnlen)6);
zgbrfs_(trans, &n, &kl, &ku, &nrhs, &a[1],
&lda, &afac[1], &ldafac, &iwork[
1], &b[1], &ldb, &x[1], &ldb, &
rwork[1], &rwork[nrhs + 1], &work[
1], &rwork[(nrhs << 1) + 1], &
info);
/* Check error code from ZGBRFS. */
if (info != 0) {
alaerh_(path, "ZGBRFS", &info, &c__0,
trans, &n, &n, &kl, &ku, &
nrhs, &imat, &nfail, &nerrs,
nout);
}
zget04_(&n, &nrhs, &x[1], &ldb, &xact[1],
&ldb, &rcondc, &result[3]);
zgbt05_(trans, &n, &kl, &ku, &nrhs, &a[1],
&lda, &b[1], &ldb, &x[1], &ldb, &
xact[1], &ldb, &rwork[1], &rwork[
nrhs + 1], &result[4]);
/* Print information about the tests that did */
/* not pass the threshold. */
for (k = 2; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___59.ciunit = *nout;
s_wsfe(&io___59);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&kl, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nrhs, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&k, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[k -
1], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
/* L60: */
}
nrun += 5;
/* L70: */
}
/* L80: */
}
/* + TEST 7: */
/* Get an estimate of RCOND = 1/CNDNUM. */
L90:
for (itran = 1; itran <= 2; ++itran) {
if (itran == 1) {
anorm = anormo;
rcondc = rcondo;
*(unsigned char *)norm = 'O';
} else {
anorm = anormi;
rcondc = rcondi;
*(unsigned char *)norm = 'I';
}
s_copy(srnamc_1.srnamt, "ZGBCON", (ftnlen)6, (
ftnlen)6);
zgbcon_(norm, &n, &kl, &ku, &afac[1], &ldafac,
&iwork[1], &anorm, &rcond, &work[1],
&rwork[1], &info);
/* Check error code from ZGBCON. */
if (info != 0) {
alaerh_(path, "ZGBCON", &info, &c__0,
norm, &n, &n, &kl, &ku, &c_n1, &
imat, &nfail, &nerrs, nout);
}
result[6] = dget06_(&rcond, &rcondc);
/* Print information about the tests that did */
/* not pass the threshold. */
if (result[6] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___61.ciunit = *nout;
s_wsfe(&io___61);
do_fio(&c__1, norm, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&imat, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&c__7, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[6], (ftnlen)
sizeof(doublereal));
e_wsfe();
++nfail;
}
++nrun;
/* L100: */
}
L110:
;
}
L120:
;
}
L130:
;
}
/* L140: */
}
/* L150: */
}
/* L160: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of ZCHKGB */
} /* zchkgb_ */
/* Subroutine */
int zgbrfsx_(char *trans, char *equed, integer *n, integer * kl, integer *ku, integer *nrhs, doublecomplex *ab, integer *ldab, doublecomplex *afb, integer *ldafb, integer *ipiv, doublereal *r__, doublereal *c__, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *berr, integer * n_err_bnds__, doublereal *err_bnds_norm__, doublereal * err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex * work, doublereal *rwork, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, x_dim1, x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, err_bnds_comp_dim1, err_bnds_comp_offset, i__1;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal illrcond_thresh__, unstable_thresh__, err_lbnd__;
integer ref_type__;
extern integer ilatrans_(char *);
integer j;
doublereal rcond_tmp__;
integer prec_type__, trans_type__;
doublereal cwise_wrong__;
extern /* Subroutine */
int zla_gbrfsx_extended_(integer *, integer *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, logical *, doublereal *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, doublecomplex *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, logical *, integer *);
char norm[1];
logical ignore_cwise__;
extern logical lsame_(char *, char *);
doublereal anorm;
extern doublereal zla_gbrcond_c_(char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer * , doublereal *, logical *, integer *, doublecomplex *, doublereal *), zla_gbrcond_x_(char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublereal *), dlamch_(char *);
extern /* Subroutine */
int xerbla_(char *, integer *);
extern doublereal zlangb_(char *, integer *, integer *, integer *, doublecomplex *, integer *, doublereal *);
extern /* Subroutine */
int zgbcon_(char *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *);
logical colequ, notran, rowequ;
extern integer ilaprec_(char *);
integer ithresh, n_norms__;
doublereal rthresh;
/* -- LAPACK computational routine (version 3.4.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* April 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Check the input parameters. */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1;
err_bnds_norm__ -= err_bnds_norm_offset;
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
afb_dim1 = *ldafb;
afb_offset = 1 + afb_dim1;
afb -= afb_offset;
--ipiv;
--r__;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--berr;
--params;
--work;
--rwork;
/* Function Body */
*info = 0;
trans_type__ = ilatrans_(trans);
ref_type__ = 1;
if (*nparams >= 1)
{
if (params[1] < 0.)
{
params[1] = 1.;
}
else
{
ref_type__ = (integer) params[1];
}
}
/* Set default parameters. */
illrcond_thresh__ = (doublereal) (*n) * dlamch_("Epsilon");
ithresh = 10;
rthresh = .5;
unstable_thresh__ = .25;
ignore_cwise__ = FALSE_;
if (*nparams >= 2)
{
if (params[2] < 0.)
{
params[2] = (doublereal) ithresh;
}
else
{
ithresh = (integer) params[2];
}
}
if (*nparams >= 3)
{
if (params[3] < 0.)
{
if (ignore_cwise__)
{
params[3] = 0.;
}
else
{
params[3] = 1.;
}
}
else
{
ignore_cwise__ = params[3] == 0.;
}
}
if (ref_type__ == 0 || *n_err_bnds__ == 0)
{
n_norms__ = 0;
}
else if (ignore_cwise__)
{
n_norms__ = 1;
}
else
{
n_norms__ = 2;
}
notran = lsame_(trans, "N");
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
/* Test input parameters. */
if (trans_type__ == -1)
{
*info = -1;
}
else if (! rowequ && ! colequ && ! lsame_(equed, "N"))
{
*info = -2;
}
else if (*n < 0)
{
*info = -3;
}
else if (*kl < 0)
{
*info = -4;
}
else if (*ku < 0)
{
*info = -5;
}
else if (*nrhs < 0)
{
*info = -6;
}
else if (*ldab < *kl + *ku + 1)
{
*info = -8;
}
else if (*ldafb < (*kl << 1) + *ku + 1)
{
*info = -10;
}
else if (*ldb < max(1,*n))
{
*info = -13;
}
else if (*ldx < max(1,*n))
{
*info = -15;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("ZGBRFSX", &i__1);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *nrhs == 0)
{
*rcond = 1.;
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
berr[j] = 0.;
if (*n_err_bnds__ >= 1)
{
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.;
}
if (*n_err_bnds__ >= 2)
{
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.;
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.;
}
if (*n_err_bnds__ >= 3)
{
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.;
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.;
}
}
return 0;
}
/* Default to failure. */
*rcond = 0.;
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
berr[j] = 1.;
if (*n_err_bnds__ >= 1)
{
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.;
}
if (*n_err_bnds__ >= 2)
{
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.;
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.;
}
if (*n_err_bnds__ >= 3)
{
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.;
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.;
}
}
/* Compute the norm of A and the reciprocal of the condition */
/* number of A. */
if (notran)
{
*(unsigned char *)norm = 'I';
}
else
{
*(unsigned char *)norm = '1';
}
anorm = zlangb_(norm, n, kl, ku, &ab[ab_offset], ldab, &rwork[1]);
zgbcon_(norm, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], &anorm, rcond, &work[1], &rwork[1], info);
/* Perform refinement on each right-hand side */
if (ref_type__ != 0)
{
prec_type__ = ilaprec_("E");
if (notran)
{
zla_gbrfsx_extended_(&prec_type__, &trans_type__, n, kl, ku, nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, & ipiv[1], &colequ, &c__[1], &b[b_offset], ldb, &x[x_offset] , ldx, &berr[1], &n_norms__, &err_bnds_norm__[ err_bnds_norm_offset], &err_bnds_comp__[ err_bnds_comp_offset], &work[1], &rwork[1], &work[*n + 1], &rwork[1], rcond, &ithresh, &rthresh, &unstable_thresh__, &ignore_cwise__, info);
}
else
{
zla_gbrfsx_extended_(&prec_type__, &trans_type__, n, kl, ku, nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, & ipiv[1], &rowequ, &r__[1], &b[b_offset], ldb, &x[x_offset] , ldx, &berr[1], &n_norms__, &err_bnds_norm__[ err_bnds_norm_offset], &err_bnds_comp__[ err_bnds_comp_offset], &work[1], &rwork[1], &work[*n + 1], &rwork[1], rcond, &ithresh, &rthresh, &unstable_thresh__, &ignore_cwise__, info);
}
}
/* Computing MAX */
d__1 = 10.;
d__2 = sqrt((doublereal) (*n)); // , expr subst
err_lbnd__ = max(d__1,d__2) * dlamch_("Epsilon");
if (*n_err_bnds__ >= 1 && n_norms__ >= 1)
{
/* Compute scaled normwise condition number cond(A*C). */
if (colequ && notran)
{
rcond_tmp__ = zla_gbrcond_c_(trans, n, kl, ku, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &ipiv[1], &c__[1], &c_true, info, &work[1], &rwork[1]);
}
else if (rowequ && ! notran)
{
rcond_tmp__ = zla_gbrcond_c_(trans, n, kl, ku, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &ipiv[1], &r__[1], &c_true, info, &work[1], &rwork[1]);
}
else
{
rcond_tmp__ = zla_gbrcond_c_(trans, n, kl, ku, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &ipiv[1], &c__[1], & c_false, info, &work[1], &rwork[1]);
}
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
/* Cap the error at 1.0. */
if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] > 1.)
{
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.;
}
/* Threshold the error (see LAWN). */
if (rcond_tmp__ < illrcond_thresh__)
{
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.;
err_bnds_norm__[j + err_bnds_norm_dim1] = 0.;
if (*info <= *n)
{
*info = *n + j;
}
}
else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < err_lbnd__)
{
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__;
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.;
}
/* Save the condition number. */
if (*n_err_bnds__ >= 3)
{
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__;
}
}
}
if (*n_err_bnds__ >= 1 && n_norms__ >= 2)
{
/* Compute componentwise condition number cond(A*diag(Y(:,J))) for */
/* each right-hand side using the current solution as an estimate of */
/* the true solution. If the componentwise error estimate is too */
/* large, then the solution is a lousy estimate of truth and the */
/* estimated RCOND may be too optimistic. To avoid misleading users, */
/* the inverse condition number is set to 0.0 when the estimated */
/* cwise error is at least CWISE_WRONG. */
cwise_wrong__ = sqrt(dlamch_("Epsilon"));
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < cwise_wrong__)
{
rcond_tmp__ = zla_gbrcond_x_(trans, n, kl, ku, &ab[ab_offset] , ldab, &afb[afb_offset], ldafb, &ipiv[1], &x[j * x_dim1 + 1], info, &work[1], &rwork[1]);
}
else
{
rcond_tmp__ = 0.;
}
/* Cap the error at 1.0. */
if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] > 1.)
{
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.;
}
/* Threshold the error (see LAWN). */
if (rcond_tmp__ < illrcond_thresh__)
{
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.;
err_bnds_comp__[j + err_bnds_comp_dim1] = 0.;
if (params[3] == 1. && *info < *n + j)
{
*info = *n + j;
}
}
else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < err_lbnd__)
{
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.;
}
/* Save the condition number. */
if (*n_err_bnds__ >= 3)
{
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__;
}
}
}
return 0;
/* End of ZGBRFSX */
}
/* Subroutine */ int zgbrfsx_(char *trans, char *equed, integer *n, integer *
kl, integer *ku, integer *nrhs, doublecomplex *ab, integer *ldab,
doublecomplex *afb, integer *ldafb, integer *ipiv, doublereal *r__,
doublereal *c__, doublecomplex *b, integer *ldb, doublecomplex *x,
integer *ldx, doublereal *rcond, doublereal *berr, integer *
n_err_bnds__, doublereal *err_bnds_norm__, doublereal *
err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex *
work, doublereal *rwork, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
x_dim1, x_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
err_bnds_comp_dim1, err_bnds_comp_offset, i__1;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal illrcond_thresh__, unstable_thresh__, err_lbnd__;
integer ref_type__;
extern integer ilatrans_(char *);
integer j;
doublereal rcond_tmp__;
integer prec_type__, trans_type__;
doublereal cwise_wrong__;
extern /* Subroutine */ int zla_gbrfsx_extended__(integer *, integer *,
integer *, integer *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, integer *, logical *,
doublereal *, doublecomplex *, integer *, doublecomplex *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, doublecomplex *, doublecomplex *,
doublereal *, integer *, doublereal *, doublereal *, logical *,
integer *);
char norm[1];
logical ignore_cwise__;
extern logical lsame_(char *, char *);
doublereal anorm;
extern doublereal zla_gbrcond_c__(char *, integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *
, doublereal *, logical *, integer *, doublecomplex *, doublereal
*, ftnlen), zla_gbrcond_x__(char *, integer *, integer *, integer
*, doublecomplex *, integer *, doublecomplex *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublereal *, ftnlen), dlamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern doublereal zlangb_(char *, integer *, integer *, integer *,
doublecomplex *, integer *, doublereal *);
extern /* Subroutine */ int zgbcon_(char *, integer *, integer *, integer
*, doublecomplex *, integer *, integer *, doublereal *,
doublereal *, doublecomplex *, doublereal *, integer *);
logical colequ, notran, rowequ;
extern integer ilaprec_(char *);
integer ithresh, n_norms__;
doublereal rthresh;
/* -- LAPACK routine (version 3.2.1) -- */
/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/* -- Jason Riedy of Univ. of California Berkeley. -- */
/* -- April 2009 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley and NAG Ltd. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGBRFSX improves the computed solution to a system of linear */
/* equations and provides error bounds and backward error estimates */
/* for the solution. In addition to normwise error bound, the code */
/* provides maximum componentwise error bound if possible. See */
/* comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the */
/* error bounds. */
/* The original system of linear equations may have been equilibrated */
/* before calling this routine, as described by arguments EQUED, R */
/* and C below. In this case, the solution and error bounds returned */
/* are for the original unequilibrated system. */
/* Arguments */
/* ========= */
/* Some optional parameters are bundled in the PARAMS array. These */
/* settings determine how refinement is performed, but often the */
/* defaults are acceptable. If the defaults are acceptable, users */
/* can pass NPARAMS = 0 which prevents the source code from accessing */
/* the PARAMS argument. */
/* TRANS (input) CHARACTER*1 */
/* Specifies the form of the system of equations: */
/* = 'N': A * X = B (No transpose) */
/* = 'T': A**T * X = B (Transpose) */
/* = 'C': A**H * X = B (Conjugate transpose = Transpose) */
/* EQUED (input) CHARACTER*1 */
/* Specifies the form of equilibration that was done to A */
/* before calling this routine. This is needed to compute */
/* the solution and error bounds correctly. */
/* = 'N': No equilibration */
/* = 'R': Row equilibration, i.e., A has been premultiplied by */
/* diag(R). */
/* = 'C': Column equilibration, i.e., A has been postmultiplied */
/* by diag(C). */
/* = 'B': Both row and column equilibration, i.e., A has been */
/* replaced by diag(R) * A * diag(C). */
/* The right hand side B has been changed accordingly. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KL (input) INTEGER */
/* The number of subdiagonals within the band of A. KL >= 0. */
/* KU (input) INTEGER */
/* The number of superdiagonals within the band of A. KU >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* AB (input) DOUBLE PRECISION array, dimension (LDAB,N) */
/* The original band matrix A, stored in rows 1 to KL+KU+1. */
/* The j-th column of A is stored in the j-th column of the */
/* array AB as follows: */
/* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KL+KU+1. */
/* AFB (input) DOUBLE PRECISION array, dimension (LDAFB,N) */
/* Details of the LU factorization of the band matrix A, as */
/* computed by DGBTRF. U is stored as an upper triangular band */
/* matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */
/* the multipliers used during the factorization are stored in */
/* rows KL+KU+2 to 2*KL+KU+1. */
/* LDAFB (input) INTEGER */
/* The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1. */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices from DGETRF; for 1<=i<=N, row i of the */
/* matrix was interchanged with row IPIV(i). */
/* R (input or output) DOUBLE PRECISION array, dimension (N) */
/* The row scale factors for A. If EQUED = 'R' or 'B', A is */
/* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */
/* is not accessed. R is an input argument if FACT = 'F'; */
/* otherwise, R is an output argument. If FACT = 'F' and */
/* EQUED = 'R' or 'B', each element of R must be positive. */
/* If R is output, each element of R is a power of the radix. */
/* If R is input, each element of R should be a power of the radix */
/* to ensure a reliable solution and error estimates. Scaling by */
/* powers of the radix does not cause rounding errors unless the */
/* result underflows or overflows. Rounding errors during scaling */
/* lead to refining with a matrix that is not equivalent to the */
/* input matrix, producing error estimates that may not be */
/* reliable. */
/* C (input or output) DOUBLE PRECISION array, dimension (N) */
/* The column scale factors for A. If EQUED = 'C' or 'B', A is */
/* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */
/* is not accessed. C is an input argument if FACT = 'F'; */
/* otherwise, C is an output argument. If FACT = 'F' and */
/* EQUED = 'C' or 'B', each element of C must be positive. */
/* If C is output, each element of C is a power of the radix. */
/* If C is input, each element of C should be a power of the radix */
/* to ensure a reliable solution and error estimates. Scaling by */
/* powers of the radix does not cause rounding errors unless the */
/* result underflows or overflows. Rounding errors during scaling */
/* lead to refining with a matrix that is not equivalent to the */
/* input matrix, producing error estimates that may not be */
/* reliable. */
/* B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) */
/* The right hand side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by DGETRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* RCOND (output) DOUBLE PRECISION */
/* Reciprocal scaled condition number. This is an estimate of the */
/* reciprocal Skeel condition number of the matrix A after */
/* equilibration (if done). If this is less than the machine */
/* precision (in particular, if it is zero), the matrix is singular */
/* to working precision. Note that the error may still be small even */
/* if this number is very small and the matrix appears ill- */
/* conditioned. */
/* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* Componentwise relative backward error. This is the */
/* componentwise relative backward error of each solution vector X(j) */
/* (i.e., the smallest relative change in any element of A or B that */
/* makes X(j) an exact solution). */
/* N_ERR_BNDS (input) INTEGER */
/* Number of error bounds to return for each right hand side */
/* and each type (normwise or componentwise). See ERR_BNDS_NORM and */
/* ERR_BNDS_COMP below. */
/* ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* normwise relative error, which is defined as follows: */
/* Normwise relative error in the ith solution vector: */
/* max_j (abs(XTRUE(j,i) - X(j,i))) */
/* ------------------------------ */
/* max_j abs(X(j,i)) */
/* The array is indexed by the type of error information as described */
/* below. There currently are up to three pieces of information */
/* returned. */
/* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_NORM(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * dlamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * dlamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated normwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * dlamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*A, where S scales each row by a power of the */
/* radix so all absolute row sums of Z are approximately 1. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* componentwise relative error, which is defined as follows: */
/* Componentwise relative error in the ith solution vector: */
/* abs(XTRUE(j,i) - X(j,i)) */
/* max_j ---------------------- */
/* abs(X(j,i)) */
/* The array is indexed by the right-hand side i (on which the */
/* componentwise relative error depends), and the type of error */
/* information as described below. There currently are up to three */
/* pieces of information returned for each right-hand side. If */
/* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */
/* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */
/* the first (:,N_ERR_BNDS) entries are returned. */
/* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_COMP(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * dlamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * dlamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated componentwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * dlamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*(A*diag(x)), where x is the solution for the */
/* current right-hand side and S scales each row of */
/* A*diag(x) by a power of the radix so all absolute row */
/* sums of Z are approximately 1. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* NPARAMS (input) INTEGER */
/* Specifies the number of parameters set in PARAMS. If .LE. 0, the */
/* PARAMS array is never referenced and default values are used. */
/* PARAMS (input / output) DOUBLE PRECISION array, dimension NPARAMS */
/* Specifies algorithm parameters. If an entry is .LT. 0.0, then */
/* that entry will be filled with default value used for that */
/* parameter. Only positions up to NPARAMS are accessed; defaults */
/* are used for higher-numbered parameters. */
/* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */
/* refinement or not. */
/* Default: 1.0D+0 */
/* = 0.0 : No refinement is performed, and no error bounds are */
/* computed. */
/* = 1.0 : Use the double-precision refinement algorithm, */
/* possibly with doubled-single computations if the */
/* compilation environment does not support DOUBLE */
/* PRECISION. */
/* (other values are reserved for future use) */
/* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */
/* computations allowed for refinement. */
/* Default: 10 */
/* Aggressive: Set to 100 to permit convergence using approximate */
/* factorizations or factorizations other than LU. If */
/* the factorization uses a technique other than */
/* Gaussian elimination, the guarantees in */
/* err_bnds_norm and err_bnds_comp may no longer be */
/* trustworthy. */
/* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */
/* will attempt to find a solution with small componentwise */
/* relative error in the double-precision algorithm. Positive */
/* is true, 0.0 is false. */
/* Default: 1.0 (attempt componentwise convergence) */
/* WORK (workspace) COMPLEX*16 array, dimension (2*N) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: Successful exit. The solution to every right-hand side is */
/* guaranteed. */
/* < 0: If INFO = -i, the i-th argument had an illegal value */
/* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */
/* has been completed, but the factor U is exactly singular, so */
/* the solution and error bounds could not be computed. RCOND = 0 */
/* is returned. */
/* = N+J: The solution corresponding to the Jth right-hand side is */
/* not guaranteed. The solutions corresponding to other right- */
/* hand sides K with K > J may not be guaranteed as well, but */
/* only the first such right-hand side is reported. If a small */
/* componentwise error is not requested (PARAMS(3) = 0.0) then */
/* the Jth right-hand side is the first with a normwise error */
/* bound that is not guaranteed (the smallest J such */
/* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */
/* the Jth right-hand side is the first with either a normwise or */
/* componentwise error bound that is not guaranteed (the smallest */
/* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */
/* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */
/* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */
/* about all of the right-hand sides check ERR_BNDS_NORM or */
/* ERR_BNDS_COMP. */
/* ================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Check the input parameters. */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1;
err_bnds_norm__ -= err_bnds_norm_offset;
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
afb_dim1 = *ldafb;
afb_offset = 1 + afb_dim1;
afb -= afb_offset;
--ipiv;
--r__;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--berr;
--params;
--work;
--rwork;
/* Function Body */
*info = 0;
trans_type__ = ilatrans_(trans);
ref_type__ = 1;
if (*nparams >= 1) {
if (params[1] < 0.) {
params[1] = 1.;
} else {
ref_type__ = (integer) params[1];
}
}
/* Set default parameters. */
illrcond_thresh__ = (doublereal) (*n) * dlamch_("Epsilon");
ithresh = 10;
rthresh = .5;
unstable_thresh__ = .25;
ignore_cwise__ = FALSE_;
if (*nparams >= 2) {
if (params[2] < 0.) {
params[2] = (doublereal) ithresh;
} else {
ithresh = (integer) params[2];
}
}
if (*nparams >= 3) {
if (params[3] < 0.) {
if (ignore_cwise__) {
params[3] = 0.;
} else {
params[3] = 1.;
}
} else {
ignore_cwise__ = params[3] == 0.;
}
}
if (ref_type__ == 0 || *n_err_bnds__ == 0) {
n_norms__ = 0;
} else if (ignore_cwise__) {
n_norms__ = 1;
} else {
n_norms__ = 2;
}
notran = lsame_(trans, "N");
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
/* Test input parameters. */
if (trans_type__ == -1) {
*info = -1;
} else if (! rowequ && ! colequ && ! lsame_(equed, "N")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*kl < 0) {
*info = -4;
} else if (*ku < 0) {
*info = -5;
} else if (*nrhs < 0) {
*info = -6;
} else if (*ldab < *kl + *ku + 1) {
*info = -8;
} else if (*ldafb < (*kl << 1) + *ku + 1) {
*info = -10;
} else if (*ldb < max(1,*n)) {
*info = -13;
} else if (*ldx < max(1,*n)) {
*info = -15;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGBRFSX", &i__1);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *nrhs == 0) {
*rcond = 1.;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
berr[j] = 0.;
if (*n_err_bnds__ >= 1) {
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.;
} else if (*n_err_bnds__ >= 2) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.;
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.;
} else if (*n_err_bnds__ >= 3) {
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.;
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.;
}
}
return 0;
}
/* Default to failure. */
*rcond = 0.;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
berr[j] = 1.;
if (*n_err_bnds__ >= 1) {
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.;
} else if (*n_err_bnds__ >= 2) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.;
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.;
} else if (*n_err_bnds__ >= 3) {
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.;
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.;
}
}
/* Compute the norm of A and the reciprocal of the condition */
/* number of A. */
if (notran) {
*(unsigned char *)norm = 'I';
} else {
*(unsigned char *)norm = '1';
}
anorm = zlangb_(norm, n, kl, ku, &ab[ab_offset], ldab, &rwork[1]);
zgbcon_(norm, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], &anorm, rcond,
&work[1], &rwork[1], info);
/* Perform refinement on each right-hand side */
if (ref_type__ != 0) {
prec_type__ = ilaprec_("E");
if (notran) {
zla_gbrfsx_extended__(&prec_type__, &trans_type__, n, kl, ku,
nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &
ipiv[1], &colequ, &c__[1], &b[b_offset], ldb, &x[x_offset]
, ldx, &berr[1], &n_norms__, &err_bnds_norm__[
err_bnds_norm_offset], &err_bnds_comp__[
err_bnds_comp_offset], &work[1], &rwork[1], &work[*n + 1],
(doublecomplex *)(&rwork[1]), rcond, &ithresh, &rthresh, &unstable_thresh__, &
ignore_cwise__, info);
} else {
zla_gbrfsx_extended__(&prec_type__, &trans_type__, n, kl, ku,
nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &
ipiv[1], &rowequ, &r__[1], &b[b_offset], ldb, &x[x_offset]
, ldx, &berr[1], &n_norms__, &err_bnds_norm__[
err_bnds_norm_offset], &err_bnds_comp__[
err_bnds_comp_offset], &work[1], &rwork[1], &work[*n + 1],
(doublecomplex *)(&rwork[1]), rcond, &ithresh, &rthresh, &unstable_thresh__, &
ignore_cwise__, info);
}
}
/* Computing MAX */
d__1 = 10., d__2 = sqrt((doublereal) (*n));
err_lbnd__ = max(d__1,d__2) * dlamch_("Epsilon");
if (*n_err_bnds__ >= 1 && n_norms__ >= 1) {
/* Compute scaled normwise condition number cond(A*C). */
if (colequ && notran) {
rcond_tmp__ = zla_gbrcond_c__(trans, n, kl, ku, &ab[ab_offset],
ldab, &afb[afb_offset], ldafb, &ipiv[1], &c__[1], &c_true,
info, &work[1], &rwork[1], (ftnlen)1);
} else if (rowequ && ! notran) {
rcond_tmp__ = zla_gbrcond_c__(trans, n, kl, ku, &ab[ab_offset],
ldab, &afb[afb_offset], ldafb, &ipiv[1], &r__[1], &c_true,
info, &work[1], &rwork[1], (ftnlen)1);
} else {
rcond_tmp__ = zla_gbrcond_c__(trans, n, kl, ku, &ab[ab_offset],
ldab, &afb[afb_offset], ldafb, &ipiv[1], &c__[1], &
c_false, info, &work[1], &rwork[1], (ftnlen)1);
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
/* Cap the error at 1.0. */
if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1
<< 1)] > 1.) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.;
}
/* Threshold the error (see LAWN). */
if (rcond_tmp__ < illrcond_thresh__) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.;
err_bnds_norm__[j + err_bnds_norm_dim1] = 0.;
if (*info <= *n) {
*info = *n + j;
}
} else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] <
err_lbnd__) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__;
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.;
}
/* Save the condition number. */
if (*n_err_bnds__ >= 3) {
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__;
}
}
}
if (*n_err_bnds__ >= 1 && n_norms__ >= 2) {
/* Compute componentwise condition number cond(A*diag(Y(:,J))) for */
/* each right-hand side using the current solution as an estimate of */
/* the true solution. If the componentwise error estimate is too */
/* large, then the solution is a lousy estimate of truth and the */
/* estimated RCOND may be too optimistic. To avoid misleading users, */
/* the inverse condition number is set to 0.0 when the estimated */
/* cwise error is at least CWISE_WRONG. */
cwise_wrong__ = sqrt(dlamch_("Epsilon"));
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] <
cwise_wrong__) {
rcond_tmp__ = zla_gbrcond_x__(trans, n, kl, ku, &ab[ab_offset]
, ldab, &afb[afb_offset], ldafb, &ipiv[1], &x[j *
x_dim1 + 1], info, &work[1], &rwork[1], (ftnlen)1);
} else {
rcond_tmp__ = 0.;
}
/* Cap the error at 1.0. */
if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1
<< 1)] > 1.) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.;
}
/* Threshold the error (see LAWN). */
if (rcond_tmp__ < illrcond_thresh__) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.;
err_bnds_comp__[j + err_bnds_comp_dim1] = 0.;
if (params[3] == 1. && *info < *n + j) {
*info = *n + j;
}
} else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] <
err_lbnd__) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.;
}
/* Save the condition number. */
if (*n_err_bnds__ >= 3) {
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__;
}
}
}
return 0;
/* End of ZGBRFSX */
} /* zgbrfsx_ */