/* Subroutine */ int zdrvpt_(logical *dotype, integer *nn, integer *nval,
integer *nrhs, doublereal *thresh, logical *tsterr, doublecomplex *a,
doublereal *d__, doublecomplex *e, doublecomplex *b, doublecomplex *x,
doublecomplex *xact, doublecomplex *work, doublereal *rwork, integer
*nout)
{
/* Initialized data */
static integer iseedy[4] = { 0,0,0,1 };
/* Format strings */
static char fmt_9999[] = "(1x,a6,\002, N =\002,i5,\002, type \002,i2,"
"\002, test \002,i2,\002, ratio = \002,g12.5)";
static char fmt_9998[] = "(1x,a6,\002, FACT='\002,a1,\002', N =\002,i5"
",\002, type \002,i2,\002, test \002,i2,\002, ratio = \002,g12.5)";
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
double z_abs(doublecomplex *);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, j, k, n;
doublereal z__[3];
integer k1, ia, in, kl, ku, ix, nt, lda;
char fact[1];
doublereal cond;
integer mode;
doublereal dmax__;
integer imat, info;
char path[3], dist[1], type__[1];
integer nrun, ifact;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
integer nfail, iseed[4];
extern doublereal dget06_(doublereal *, doublereal *);
doublereal rcond;
integer nimat;
doublereal anorm;
extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *
), dcopy_(integer *, doublereal *, integer *, doublereal *,
integer *);
integer izero, nerrs;
extern /* Subroutine */ int zptt01_(integer *, doublereal *,
doublecomplex *, doublereal *, doublecomplex *, doublecomplex *,
doublereal *);
logical zerot;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zptt02_(char *, integer *, integer *,
doublereal *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *), zptt05_(
integer *, integer *, doublereal *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublereal *), zptsv_(integer *, integer *, doublereal *,
doublecomplex *, doublecomplex *, integer *, integer *), zlatb4_(
char *, integer *, integer *, integer *, char *, integer *,
integer *, doublereal *, integer *, doublereal *, char *), aladhd_(integer *, char *), alaerh_(char
*, char *, integer *, integer *, char *, integer *, integer *,
integer *, integer *, integer *, integer *, integer *, integer *,
integer *);
extern integer idamax_(integer *, doublereal *, integer *);
doublereal rcondc;
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *), alasvm_(char *, integer *, integer *,
integer *, integer *), dlarnv_(integer *, integer *,
integer *, doublereal *);
doublereal ainvnm;
extern doublereal zlanht_(char *, integer *, doublereal *, doublecomplex *
);
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
extern doublereal dzasum_(integer *, doublecomplex *, integer *);
extern /* Subroutine */ int zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlaptm_(char *, integer *, integer *, doublereal *,
doublereal *, doublecomplex *, doublecomplex *, integer *,
doublereal *, doublecomplex *, integer *), zlatms_(
integer *, integer *, char *, integer *, char *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *, char
*, doublecomplex *, integer *, doublecomplex *, integer *), zlarnv_(integer *, integer *, integer *,
doublecomplex *);
doublereal result[6];
extern /* Subroutine */ int zpttrf_(integer *, doublereal *,
doublecomplex *, integer *), zerrvx_(char *, integer *),
zpttrs_(char *, integer *, integer *, doublereal *, doublecomplex
*, doublecomplex *, integer *, integer *), zptsvx_(char *,
integer *, integer *, doublereal *, doublecomplex *, doublereal *
, doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *);
/* Fortran I/O blocks */
static cilist io___35 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___38 = { 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 */
/* ======= */
/* ZDRVPT tests ZPTSV and -SVX. */
/* 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. */
/* 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. */
/* NRHS (input) INTEGER */
/* The number of right hand side vectors to be generated for */
/* each linear system. */
/* 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 (NMAX*2) */
/* D (workspace) DOUBLE PRECISION array, dimension (NMAX*2) */
/* E (workspace) COMPLEX*16 array, dimension (NMAX*2) */
/* B (workspace) COMPLEX*16 array, dimension (NMAX*NRHS) */
/* X (workspace) COMPLEX*16 array, dimension (NMAX*NRHS) */
/* XACT (workspace) COMPLEX*16 array, dimension (NMAX*NRHS) */
/* WORK (workspace) COMPLEX*16 array, dimension */
/* (NMAX*max(3,NRHS)) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (NMAX+2*NRHS) */
/* 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 */
--rwork;
--work;
--xact;
--x;
--b;
--e;
--d__;
--a;
--nval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "PT", (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) {
zerrvx_(path, nout);
}
infoc_1.infot = 0;
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
/* Do for each value of N in NVAL. */
n = nval[in];
lda = max(1,n);
nimat = 12;
if (n <= 0) {
nimat = 1;
}
i__2 = nimat;
for (imat = 1; imat <= i__2; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (n > 0 && ! dotype[imat]) {
goto L110;
}
/* Set up parameters with ZLATB4. */
zlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &
cond, dist);
zerot = imat >= 8 && imat <= 10;
if (imat <= 6) {
/* Type 1-6: generate a symmetric tridiagonal matrix of */
/* known condition number in lower triangular band storage. */
s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)6, (ftnlen)6);
zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cond,
&anorm, &kl, &ku, "B", &a[1], &c__2, &work[1], &info);
/* Check the error code from ZLATMS. */
if (info != 0) {
alaerh_(path, "ZLATMS", &info, &c__0, " ", &n, &n, &kl, &
ku, &c_n1, &imat, &nfail, &nerrs, nout);
goto L110;
}
izero = 0;
/* Copy the matrix to D and E. */
ia = 1;
i__3 = n - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
i__5 = ia;
d__[i__4] = a[i__5].r;
i__4 = i__;
i__5 = ia + 1;
e[i__4].r = a[i__5].r, e[i__4].i = a[i__5].i;
ia += 2;
/* L20: */
}
if (n > 0) {
i__3 = n;
i__4 = ia;
d__[i__3] = a[i__4].r;
}
} else {
/* Type 7-12: generate a diagonally dominant matrix with */
/* unknown condition number in the vectors D and E. */
if (! zerot || ! dotype[7]) {
/* Let D and E have values from [-1,1]. */
dlarnv_(&c__2, iseed, &n, &d__[1]);
i__3 = n - 1;
zlarnv_(&c__2, iseed, &i__3, &e[1]);
/* Make the tridiagonal matrix diagonally dominant. */
if (n == 1) {
d__[1] = abs(d__[1]);
} else {
d__[1] = abs(d__[1]) + z_abs(&e[1]);
d__[n] = (d__1 = d__[n], abs(d__1)) + z_abs(&e[n - 1])
;
i__3 = n - 1;
for (i__ = 2; i__ <= i__3; ++i__) {
d__[i__] = (d__1 = d__[i__], abs(d__1)) + z_abs(&
e[i__]) + z_abs(&e[i__ - 1]);
/* L30: */
}
}
/* Scale D and E so the maximum element is ANORM. */
ix = idamax_(&n, &d__[1], &c__1);
dmax__ = d__[ix];
d__1 = anorm / dmax__;
dscal_(&n, &d__1, &d__[1], &c__1);
if (n > 1) {
i__3 = n - 1;
d__1 = anorm / dmax__;
zdscal_(&i__3, &d__1, &e[1], &c__1);
}
} else if (izero > 0) {
/* Reuse the last matrix by copying back the zeroed out */
/* elements. */
if (izero == 1) {
d__[1] = z__[1];
if (n > 1) {
e[1].r = z__[2], e[1].i = 0.;
}
} else if (izero == n) {
i__3 = n - 1;
e[i__3].r = z__[0], e[i__3].i = 0.;
d__[n] = z__[1];
} else {
i__3 = izero - 1;
e[i__3].r = z__[0], e[i__3].i = 0.;
d__[izero] = z__[1];
i__3 = izero;
e[i__3].r = z__[2], e[i__3].i = 0.;
}
}
/* For types 8-10, set one row and column of the matrix to */
/* zero. */
izero = 0;
if (imat == 8) {
izero = 1;
z__[1] = d__[1];
d__[1] = 0.;
if (n > 1) {
z__[2] = e[1].r;
e[1].r = 0., e[1].i = 0.;
}
} else if (imat == 9) {
izero = n;
if (n > 1) {
i__3 = n - 1;
z__[0] = e[i__3].r;
i__3 = n - 1;
e[i__3].r = 0., e[i__3].i = 0.;
}
z__[1] = d__[n];
d__[n] = 0.;
} else if (imat == 10) {
izero = (n + 1) / 2;
if (izero > 1) {
i__3 = izero - 1;
z__[0] = e[i__3].r;
i__3 = izero - 1;
e[i__3].r = 0., e[i__3].i = 0.;
i__3 = izero;
z__[2] = e[i__3].r;
i__3 = izero;
e[i__3].r = 0., e[i__3].i = 0.;
}
z__[1] = d__[izero];
d__[izero] = 0.;
}
}
/* Generate NRHS random solution vectors. */
ix = 1;
i__3 = *nrhs;
for (j = 1; j <= i__3; ++j) {
zlarnv_(&c__2, iseed, &n, &xact[ix]);
ix += lda;
/* L40: */
}
/* Set the right hand side. */
zlaptm_("Lower", &n, nrhs, &c_b24, &d__[1], &e[1], &xact[1], &lda,
&c_b25, &b[1], &lda);
for (ifact = 1; ifact <= 2; ++ifact) {
if (ifact == 1) {
*(unsigned char *)fact = 'F';
} else {
*(unsigned char *)fact = 'N';
}
/* Compute the condition number for comparison with */
/* the value returned by ZPTSVX. */
if (zerot) {
if (ifact == 1) {
goto L100;
}
rcondc = 0.;
} else if (ifact == 1) {
/* Compute the 1-norm of A. */
anorm = zlanht_("1", &n, &d__[1], &e[1]);
dcopy_(&n, &d__[1], &c__1, &d__[n + 1], &c__1);
if (n > 1) {
i__3 = n - 1;
zcopy_(&i__3, &e[1], &c__1, &e[n + 1], &c__1);
}
/* Factor the matrix A. */
zpttrf_(&n, &d__[n + 1], &e[n + 1], &info);
/* Use ZPTTRS to solve for one column at a time of */
/* inv(A), computing the maximum column sum as we go. */
ainvnm = 0.;
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = n;
for (j = 1; j <= i__4; ++j) {
i__5 = j;
x[i__5].r = 0., x[i__5].i = 0.;
/* L50: */
}
i__4 = i__;
x[i__4].r = 1., x[i__4].i = 0.;
zpttrs_("Lower", &n, &c__1, &d__[n + 1], &e[n + 1], &
x[1], &lda, &info);
/* Computing MAX */
d__1 = ainvnm, d__2 = dzasum_(&n, &x[1], &c__1);
ainvnm = max(d__1,d__2);
/* L60: */
}
/* Compute the 1-norm condition number of A. */
if (anorm <= 0. || ainvnm <= 0.) {
rcondc = 1.;
} else {
rcondc = 1. / anorm / ainvnm;
}
}
if (ifact == 2) {
/* --- Test ZPTSV -- */
dcopy_(&n, &d__[1], &c__1, &d__[n + 1], &c__1);
if (n > 1) {
i__3 = n - 1;
zcopy_(&i__3, &e[1], &c__1, &e[n + 1], &c__1);
}
zlacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &lda);
/* Factor A as L*D*L' and solve the system A*X = B. */
s_copy(srnamc_1.srnamt, "ZPTSV ", (ftnlen)6, (ftnlen)6);
zptsv_(&n, nrhs, &d__[n + 1], &e[n + 1], &x[1], &lda, &
info);
/* Check error code from ZPTSV . */
if (info != izero) {
alaerh_(path, "ZPTSV ", &info, &izero, " ", &n, &n, &
c__1, &c__1, nrhs, &imat, &nfail, &nerrs,
nout);
}
nt = 0;
if (izero == 0) {
/* Check the factorization by computing the ratio */
/* norm(L*D*L' - A) / (n * norm(A) * EPS ) */
zptt01_(&n, &d__[1], &e[1], &d__[n + 1], &e[n + 1], &
work[1], result);
/* Compute the residual in the solution. */
zlacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda);
zptt02_("Lower", &n, nrhs, &d__[1], &e[1], &x[1], &
lda, &work[1], &lda, &result[1]);
/* Check solution from generated exact solution. */
zget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[2]);
nt = 3;
}
/* Print information about the tests that did not pass */
/* the threshold. */
i__3 = nt;
for (k = 1; k <= i__3; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
io___35.ciunit = *nout;
s_wsfe(&io___35);
do_fio(&c__1, "ZPTSV ", (ftnlen)6);
do_fio(&c__1, (char *)&n, (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;
}
/* L70: */
}
nrun += nt;
}
/* --- Test ZPTSVX --- */
if (ifact > 1) {
/* Initialize D( N+1:2*N ) and E( N+1:2*N ) to zero. */
i__3 = n - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
d__[n + i__] = 0.;
i__4 = n + i__;
e[i__4].r = 0., e[i__4].i = 0.;
/* L80: */
}
if (n > 0) {
d__[n + n] = 0.;
}
}
zlaset_("Full", &n, nrhs, &c_b62, &c_b62, &x[1], &lda);
/* Solve the system and compute the condition number and */
/* error bounds using ZPTSVX. */
s_copy(srnamc_1.srnamt, "ZPTSVX", (ftnlen)6, (ftnlen)6);
zptsvx_(fact, &n, nrhs, &d__[1], &e[1], &d__[n + 1], &e[n + 1]
, &b[1], &lda, &x[1], &lda, &rcond, &rwork[1], &rwork[
*nrhs + 1], &work[1], &rwork[(*nrhs << 1) + 1], &info);
/* Check the error code from ZPTSVX. */
if (info != izero) {
alaerh_(path, "ZPTSVX", &info, &izero, fact, &n, &n, &
c__1, &c__1, nrhs, &imat, &nfail, &nerrs, nout);
}
if (izero == 0) {
if (ifact == 2) {
/* Check the factorization by computing the ratio */
/* norm(L*D*L' - A) / (n * norm(A) * EPS ) */
k1 = 1;
zptt01_(&n, &d__[1], &e[1], &d__[n + 1], &e[n + 1], &
work[1], result);
} else {
k1 = 2;
}
/* Compute the residual in the solution. */
zlacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda);
zptt02_("Lower", &n, nrhs, &d__[1], &e[1], &x[1], &lda, &
work[1], &lda, &result[1]);
/* Check solution from generated exact solution. */
zget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &
result[2]);
/* Check error bounds from iterative refinement. */
zptt05_(&n, nrhs, &d__[1], &e[1], &b[1], &lda, &x[1], &
lda, &xact[1], &lda, &rwork[1], &rwork[*nrhs + 1],
&result[3]);
} else {
k1 = 6;
}
/* Check the reciprocal of the condition number. */
result[5] = dget06_(&rcond, &rcondc);
/* Print information about the tests that did not pass */
/* the threshold. */
for (k = k1; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
io___38.ciunit = *nout;
s_wsfe(&io___38);
do_fio(&c__1, "ZPTSVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, (char *)&n, (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;
}
/* L90: */
}
nrun = nrun + 7 - k1;
L100:
;
}
L110:
;
}
/* L120: */
}
/* Print a summary of the results. */
alasvm_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of ZDRVPT */
} /* zdrvpt_ */
/* Subroutine */ int zptsvx_(char *fact, integer *n, integer *nrhs,
doublereal *d__, doublecomplex *e, doublereal *df, doublecomplex *ef,
doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx,
doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *
work, doublereal *rwork, integer *info)
{
/* -- LAPACK 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
=======
ZPTSVX uses the factorization A = L*D*L**H to compute the solution
to a complex system of linear equations A*X = B, where A is an
N-by-N Hermitian positive definite tridiagonal matrix and X and B
are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the matrix A is factored as A = L*D*L**H, where L
is a unit lower bidiagonal matrix and D is diagonal. The
factorization can also be regarded as having the form
A = U**H*D*U.
2. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
Arguments
=========
FACT (input) CHARACTER*1
Specifies whether or not the factored form of the matrix
A is supplied on entry.
= 'F': On entry, DF and EF contain the factored form of A.
D, E, DF, and EF will not be modified.
= 'N': The matrix A will be copied to DF and EF and
factored.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
D (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.
E (input) COMPLEX*16 array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A.
DF (input or output) DOUBLE PRECISION array, dimension (N)
If FACT = 'F', then DF is an input argument and on entry
contains the n diagonal elements of the diagonal matrix D
from the L*D*L**H factorization of A.
If FACT = 'N', then DF is an output argument and on exit
contains the n diagonal elements of the diagonal matrix D
from the L*D*L**H factorization of A.
EF (input or output) COMPLEX*16 array, dimension (N-1)
If FACT = 'F', then EF is an input argument and on entry
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**H factorization of A.
If FACT = 'N', then EF is an output argument and on exit
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**H factorization of A.
B (input) COMPLEX*16 array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (output) COMPLEX*16 array, dimension (LDX,NRHS)
If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
RCOND (output) DOUBLE PRECISION
The reciprocal condition number of the matrix A. If RCOND
is less than the machine precision (in particular, if
RCOND = 0), the matrix is singular to working precision.
This condition is indicated by a return code of INFO > 0.
FERR (output) DOUBLE PRECISION array, dimension (NRHS)
The forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j).
BERR (output) DOUBLE PRECISION array, dimension (NRHS)
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).
WORK (workspace) COMPLEX*16 array, dimension (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
> 0: if INFO = i, and i is
<= N: the leading minor of order i of A is
not positive definite, so the factorization
could not be completed, and the solution has not
been computed. RCOND = 0 is returned.
= N+1: U is nonsingular, but RCOND is less than machine
precision, meaning that the matrix is singular
to working precision. Nevertheless, the
solution and error bounds are computed because
there are a number of situations where the
computed solution can be more accurate than the
value of RCOND would suggest.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
static doublereal anorm;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), zcopy_(integer *, doublecomplex *,
integer *, doublecomplex *, integer *);
extern doublereal dlamch_(char *);
static logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern doublereal zlanht_(char *, integer *, doublereal *, doublecomplex *
);
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zptcon_(integer *, doublereal *, doublecomplex *, doublereal *,
doublereal *, doublereal *, integer *), zptrfs_(char *, integer *,
integer *, doublereal *, doublecomplex *, doublereal *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublecomplex *,
doublereal *, integer *), zpttrf_(integer *, doublereal *,
doublecomplex *, integer *), zpttrs_(char *, integer *, integer *
, doublereal *, doublecomplex *, doublecomplex *, integer *,
integer *);
--d__;
--e;
--df;
--ef;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
if (! nofact && ! lsame_(fact, "F")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < max(1,*n)) {
*info = -9;
} else if (*ldx < max(1,*n)) {
*info = -11;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPTSVX", &i__1);
return 0;
}
if (nofact) {
/* Compute the L*D*L' (or U'*D*U) factorization of A. */
dcopy_(n, &d__[1], &c__1, &df[1], &c__1);
if (*n > 1) {
i__1 = *n - 1;
zcopy_(&i__1, &e[1], &c__1, &ef[1], &c__1);
}
zpttrf_(n, &df[1], &ef[1], info);
/* Return if INFO is non-zero. */
if (*info != 0) {
if (*info > 0) {
*rcond = 0.;
}
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = zlanht_("1", n, &d__[1], &e[1]);
/* Compute the reciprocal of the condition number of A. */
zptcon_(n, &df[1], &ef[1], &anorm, rcond, &rwork[1], info);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < dlamch_("Epsilon")) {
*info = *n + 1;
}
/* Compute the solution vectors X. */
zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
zpttrs_("Lower", n, nrhs, &df[1], &ef[1], &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solutions and
compute error bounds and backward error estimates for them. */
zptrfs_("Lower", n, nrhs, &d__[1], &e[1], &df[1], &ef[1], &b[b_offset],
ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1], &rwork[1],
info);
return 0;
/* End of ZPTSVX */
} /* zptsvx_ */
