/* Subroutine */ int cerrpo_(char *path, integer *nunit)
{
/* System generated locals */
integer i__1;
real r__1, r__2;
complex q__1;
/* Local variables */
complex a[16] /* was [4][4] */, b[4];
integer i__, j;
real r__[4];
complex w[8], x[4];
char c2[2];
real r1[4], r2[4];
complex af[16] /* was [4][4] */;
integer info;
real anrm, rcond;
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CERRPO tests the error exits for the COMPLEX routines */
/* for Hermitian positive definite matrices. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Set the variables to innocuous values. */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
i__1 = i__ + (j << 2) - 5;
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = i__ + (j << 2) - 5;
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
af[i__1].r = q__1.r, af[i__1].i = q__1.i;
/* L10: */
}
i__1 = j - 1;
b[i__1].r = 0.f, b[i__1].i = 0.f;
r1[j - 1] = 0.f;
r2[j - 1] = 0.f;
i__1 = j - 1;
w[i__1].r = 0.f, w[i__1].i = 0.f;
i__1 = j - 1;
x[i__1].r = 0.f, x[i__1].i = 0.f;
/* L20: */
}
anrm = 1.f;
infoc_1.ok = TRUE_;
/* Test error exits of the routines that use the Cholesky */
/* decomposition of a Hermitian positive definite matrix. */
if (lsamen_(&c__2, c2, "PO")) {
/* CPOTRF */
s_copy(srnamc_1.srnamt, "CPOTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpotrf_("/", &c__0, a, &c__1, &info);
chkxer_("CPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpotrf_("U", &c_n1, a, &c__1, &info);
chkxer_("CPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cpotrf_("U", &c__2, a, &c__1, &info);
chkxer_("CPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPOTF2 */
s_copy(srnamc_1.srnamt, "CPOTF2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpotf2_("/", &c__0, a, &c__1, &info);
chkxer_("CPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpotf2_("U", &c_n1, a, &c__1, &info);
chkxer_("CPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cpotf2_("U", &c__2, a, &c__1, &info);
chkxer_("CPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPOTRI */
s_copy(srnamc_1.srnamt, "CPOTRI", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpotri_("/", &c__0, a, &c__1, &info);
chkxer_("CPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpotri_("U", &c_n1, a, &c__1, &info);
chkxer_("CPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cpotri_("U", &c__2, a, &c__1, &info);
chkxer_("CPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPOTRS */
s_copy(srnamc_1.srnamt, "CPOTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpotrs_("/", &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("CPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpotrs_("U", &c_n1, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("CPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpotrs_("U", &c__0, &c_n1, a, &c__1, b, &c__1, &info);
chkxer_("CPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cpotrs_("U", &c__2, &c__1, a, &c__1, b, &c__2, &info);
chkxer_("CPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cpotrs_("U", &c__2, &c__1, a, &c__2, b, &c__1, &info);
chkxer_("CPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPORFS */
s_copy(srnamc_1.srnamt, "CPORFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cporfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cporfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cporfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cporfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &c__2,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cporfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &c__2,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
cporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__1, x, &c__2,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
cporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__2, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPOCON */
s_copy(srnamc_1.srnamt, "CPOCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpocon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("CPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpocon_("U", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("CPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cpocon_("U", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("CPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
r__1 = -anrm;
cpocon_("U", &c__1, a, &c__1, &r__1, &rcond, w, r__, &info)
;
chkxer_("CPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPOEQU */
s_copy(srnamc_1.srnamt, "CPOEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpoequ_(&c_n1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("CPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpoequ_(&c__2, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("CPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Test error exits of the routines that use the Cholesky */
/* decomposition of a Hermitian positive definite packed matrix. */
} else if (lsamen_(&c__2, c2, "PP")) {
/* CPPTRF */
s_copy(srnamc_1.srnamt, "CPPTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpptrf_("/", &c__0, a, &info);
chkxer_("CPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpptrf_("U", &c_n1, a, &info);
chkxer_("CPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPPTRI */
s_copy(srnamc_1.srnamt, "CPPTRI", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpptri_("/", &c__0, a, &info);
chkxer_("CPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpptri_("U", &c_n1, a, &info);
chkxer_("CPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPPTRS */
s_copy(srnamc_1.srnamt, "CPPTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpptrs_("/", &c__0, &c__0, a, b, &c__1, &info);
chkxer_("CPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpptrs_("U", &c_n1, &c__0, a, b, &c__1, &info);
chkxer_("CPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpptrs_("U", &c__0, &c_n1, a, b, &c__1, &info);
chkxer_("CPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
cpptrs_("U", &c__2, &c__1, a, b, &c__1, &info);
chkxer_("CPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPPRFS */
s_copy(srnamc_1.srnamt, "CPPRFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpprfs_("/", &c__0, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("CPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpprfs_("U", &c_n1, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("CPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpprfs_("U", &c__0, &c_n1, a, af, b, &c__1, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("CPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cpprfs_("U", &c__2, &c__1, a, af, b, &c__1, x, &c__2, r1, r2, w, r__,
&info);
chkxer_("CPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
cpprfs_("U", &c__2, &c__1, a, af, b, &c__2, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("CPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPPCON */
s_copy(srnamc_1.srnamt, "CPPCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cppcon_("/", &c__0, a, &anrm, &rcond, w, r__, &info);
chkxer_("CPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cppcon_("U", &c_n1, a, &anrm, &rcond, w, r__, &info);
chkxer_("CPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
r__1 = -anrm;
cppcon_("U", &c__1, a, &r__1, &rcond, w, r__, &info);
chkxer_("CPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPPEQU */
s_copy(srnamc_1.srnamt, "CPPEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cppequ_("/", &c__0, a, r1, &rcond, &anrm, &info);
chkxer_("CPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cppequ_("U", &c_n1, a, r1, &rcond, &anrm, &info);
chkxer_("CPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Test error exits of the routines that use the Cholesky */
/* decomposition of a Hermitian positive definite band matrix. */
} else if (lsamen_(&c__2, c2, "PB")) {
/* CPBTRF */
s_copy(srnamc_1.srnamt, "CPBTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpbtrf_("/", &c__0, &c__0, a, &c__1, &info);
chkxer_("CPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpbtrf_("U", &c_n1, &c__0, a, &c__1, &info);
chkxer_("CPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpbtrf_("U", &c__1, &c_n1, a, &c__1, &info);
chkxer_("CPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cpbtrf_("U", &c__2, &c__1, a, &c__1, &info);
chkxer_("CPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPBTF2 */
s_copy(srnamc_1.srnamt, "CPBTF2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpbtf2_("/", &c__0, &c__0, a, &c__1, &info);
chkxer_("CPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpbtf2_("U", &c_n1, &c__0, a, &c__1, &info);
chkxer_("CPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpbtf2_("U", &c__1, &c_n1, a, &c__1, &info);
chkxer_("CPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cpbtf2_("U", &c__2, &c__1, a, &c__1, &info);
chkxer_("CPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPBTRS */
s_copy(srnamc_1.srnamt, "CPBTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpbtrs_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("CPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpbtrs_("U", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("CPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpbtrs_("U", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("CPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cpbtrs_("U", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, &info);
chkxer_("CPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
cpbtrs_("U", &c__2, &c__1, &c__1, a, &c__1, b, &c__1, &info);
chkxer_("CPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cpbtrs_("U", &c__2, &c__0, &c__1, a, &c__1, b, &c__1, &info);
chkxer_("CPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPBRFS */
s_copy(srnamc_1.srnamt, "CPBRFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpbrfs_("/", &c__0, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpbrfs_("U", &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpbrfs_("U", &c__1, &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cpbrfs_("U", &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
cpbrfs_("U", &c__2, &c__1, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cpbrfs_("U", &c__2, &c__1, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__1, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__2, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPBCON */
s_copy(srnamc_1.srnamt, "CPBCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpbcon_("/", &c__0, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("CPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpbcon_("U", &c_n1, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("CPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpbcon_("U", &c__1, &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("CPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cpbcon_("U", &c__2, &c__1, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("CPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
r__1 = -anrm;
cpbcon_("U", &c__1, &c__0, a, &c__1, &r__1, &rcond, w, r__, &info);
chkxer_("CPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPBEQU */
s_copy(srnamc_1.srnamt, "CPBEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpbequ_("/", &c__0, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("CPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpbequ_("U", &c_n1, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("CPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpbequ_("U", &c__1, &c_n1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("CPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cpbequ_("U", &c__2, &c__1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("CPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
}
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of CERRPO */
} /* cerrpo_ */
/* Subroutine */ int cppsvx_(char *fact, char *uplo, integer *n, integer *
nrhs, complex *ap, complex *afp, char *equed, real *s, complex *b,
integer *ldb, complex *x, integer *ldx, real *rcond, real *ferr, real
*berr, complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2;
complex q__1;
/* Local variables */
integer i__, j;
real amax, smin, smax;
real scond, anorm;
logical equil, rcequ;
logical nofact;
real bignum;
integer infequ;
real smlnum;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* CPPSVX uses the Cholesky factorization A = U**H*U or A = L*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 matrix stored in */
/* packed format 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 = 'E', real scaling factors are computed to equilibrate */
/* the system: */
/* diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B */
/* Whether or not the system will be equilibrated depends on the */
/* scaling of the matrix A, but if equilibration is used, A is */
/* overwritten by diag(S)*A*diag(S) and B by diag(S)*B. */
/* 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to */
/* factor the matrix A (after equilibration if FACT = 'E') as */
/* A = U'* U , if UPLO = 'U', or */
/* A = L * L', if UPLO = 'L', */
/* where U is an upper triangular matrix, L is a lower triangular */
/* matrix, and ' indicates conjugate transpose. */
/* 3. 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. */
/* 4. The system of equations is solved for X using the factored form */
/* of A. */
/* 5. Iterative refinement is applied to improve the computed solution */
/* matrix and calculate error bounds and backward error estimates */
/* for it. */
/* 6. If equilibration was used, the matrix X is premultiplied by */
/* diag(S) so that it solves the original system before */
/* equilibration. */
/* Arguments */
/* ========= */
/* FACT (input) CHARACTER*1 */
/* Specifies whether or not the factored form of the matrix A is */
/* supplied on entry, and if not, whether the matrix A should be */
/* equilibrated before it is factored. */
/* = 'F': On entry, AFP contains the factored form of A. */
/* If EQUED = 'Y', the matrix A has been equilibrated */
/* with scaling factors given by S. AP and AFP will not */
/* be modified. */
/* = 'N': The matrix A will be copied to AFP and factored. */
/* = 'E': The matrix A will be equilibrated if necessary, then */
/* copied to AFP and factored. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The number of linear equations, i.e., 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. */
/* AP (input/output) COMPLEX array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangle of the Hermitian matrix */
/* A, packed columnwise in a linear array, except if FACT = 'F' */
/* and EQUED = 'Y', then A must contain the equilibrated matrix */
/* diag(S)*A*diag(S). The j-th column of A is stored in the */
/* array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* See below for further details. A is not modified if */
/* FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. */
/* On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by */
/* diag(S)*A*diag(S). */
/* AFP (input or output) COMPLEX array, dimension (N*(N+1)/2) */
/* If FACT = 'F', then AFP is an input argument and on entry */
/* contains the triangular factor U or L from the Cholesky */
/* factorization A = U**H*U or A = L*L**H, in the same storage */
/* format as A. If EQUED .ne. 'N', then AFP is the factored */
/* form of the equilibrated matrix A. */
/* If FACT = 'N', then AFP is an output argument and on exit */
/* returns the triangular factor U or L from the Cholesky */
/* factorization A = U**H*U or A = L*L**H of the original */
/* matrix A. */
/* If FACT = 'E', then AFP is an output argument and on exit */
/* returns the triangular factor U or L from the Cholesky */
/* factorization A = U**H*U or A = L*L**H of the equilibrated */
/* matrix A (see the description of AP for the form of the */
/* equilibrated matrix). */
/* EQUED (input or output) CHARACTER*1 */
/* Specifies the form of equilibration that was done. */
/* = 'N': No equilibration (always true if FACT = 'N'). */
/* = 'Y': Equilibration was done, i.e., A has been replaced by */
/* diag(S) * A * diag(S). */
/* EQUED is an input argument if FACT = 'F'; otherwise, it is an */
/* output argument. */
/* S (input or output) REAL array, dimension (N) */
/* The scale factors for A; not accessed if EQUED = 'N'. S is */
/* an input argument if FACT = 'F'; otherwise, S is an output */
/* argument. If FACT = 'F' and EQUED = 'Y', each element of S */
/* must be positive. */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS right hand side matrix B. */
/* On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y', */
/* B is overwritten by diag(S) * B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (output) COMPLEX array, dimension (LDX,NRHS) */
/* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X to */
/* the original system of equations. Note that if EQUED = 'Y', */
/* A and B are modified on exit, and the solution to the */
/* equilibrated system is inv(diag(S))*X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* RCOND (output) REAL */
/* The estimate of the reciprocal condition number of the matrix */
/* A after equilibration (if done). 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) REAL array, dimension (NRHS) */
/* The estimated 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). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) REAL 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 array, dimension (2*N) */
/* RWORK (workspace) REAL 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. */
/* Further Details */
/* =============== */
/* The packed storage scheme is illustrated by the following example */
/* when N = 4, UPLO = 'U': */
/* Two-dimensional storage of the Hermitian matrix A: */
/* a11 a12 a13 a14 */
/* a22 a23 a24 */
/* a33 a34 (aij = conjg(aji)) */
/* a44 */
/* Packed storage of the upper triangle of A: */
/* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] */
/* ===================================================================== */
/* Parameter adjustments */
--ap;
--afp;
--s;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
if (nofact || equil) {
*(unsigned char *)equed = 'N';
rcequ = FALSE_;
} else {
rcequ = lsame_(equed, "Y");
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
}
/* Test the input parameters. */
if (! nofact && ! equil && ! lsame_(fact, "F")) {
*info = -1;
} else if (! lsame_(uplo, "U") && ! lsame_(uplo,
"L")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (lsame_(fact, "F") && ! (rcequ || lsame_(
equed, "N"))) {
*info = -7;
} else {
if (rcequ) {
smin = bignum;
smax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = smin, r__2 = s[j];
smin = dmin(r__1,r__2);
/* Computing MAX */
r__1 = smax, r__2 = s[j];
smax = dmax(r__1,r__2);
}
if (smin <= 0.f) {
*info = -8;
} else if (*n > 0) {
scond = dmax(smin,smlnum) / dmin(smax,bignum);
} else {
scond = 1.f;
}
}
if (*info == 0) {
if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldx < max(1,*n)) {
*info = -12;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPPSVX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
cppequ_(uplo, n, &ap[1], &s[1], &scond, &amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
claqhp_(uplo, n, &ap[1], &s[1], &scond, &amax, equed);
rcequ = lsame_(equed, "Y");
}
}
/* Scale the right-hand side. */
if (rcequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__;
i__5 = i__ + j * b_dim1;
q__1.r = s[i__4] * b[i__5].r, q__1.i = s[i__4] * b[i__5].i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
}
}
}
if (nofact || equil) {
/* Compute the Cholesky factorization A = U'*U or A = L*L'. */
i__1 = *n * (*n + 1) / 2;
ccopy_(&i__1, &ap[1], &c__1, &afp[1], &c__1);
cpptrf_(uplo, n, &afp[1], info);
/* Return if INFO is non-zero. */
if (*info > 0) {
*rcond = 0.f;
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = clanhp_("I", uplo, n, &ap[1], &rwork[1]);
/* Compute the reciprocal of the condition number of A. */
cppcon_(uplo, n, &afp[1], &anorm, rcond, &work[1], &rwork[1], info);
/* Compute the solution matrix X. */
clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
cpptrs_(uplo, n, nrhs, &afp[1], &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
cpprfs_(uplo, n, nrhs, &ap[1], &afp[1], &b[b_offset], ldb, &x[x_offset],
ldx, &ferr[1], &berr[1], &work[1], &rwork[1], info);
/* Transform the solution matrix X to a solution of the original */
/* system. */
if (rcequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * x_dim1;
i__4 = i__;
i__5 = i__ + j * x_dim1;
q__1.r = s[i__4] * x[i__5].r, q__1.i = s[i__4] * x[i__5].i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
}
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] /= scond;
}
}
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon")) {
*info = *n + 1;
}
return 0;
/* End of CPPSVX */
} /* cppsvx_ */
/* Subroutine */ int cpprfs_(char *uplo, integer *n, integer *nrhs, complex *
ap, complex *afp, complex *b, integer *ldb, complex *x, integer *ldx,
real *ferr, real *berr, complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer i__, j, k;
real s;
integer ik, kk;
real xk;
integer nz;
real eps;
integer kase;
real safe1, safe2;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), chpmv_(char *, integer *, complex *,
complex *, complex *, integer *, complex *, complex *, integer *), caxpy_(integer *, complex *, complex *, integer *,
complex *, integer *);
integer count;
logical upper;
extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real
*, integer *, integer *);
extern doublereal slamch_(char *);
real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *), cpptrs_(
char *, integer *, integer *, complex *, complex *, integer *,
integer *);
real lstres;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CPPRFS improves the computed solution to a system of linear */
/* equations when the coefficient matrix is Hermitian positive definite */
/* and packed, and provides error bounds and backward error estimates */
/* for the solution. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* 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. */
/* AP (input) COMPLEX array, dimension (N*(N+1)/2) */
/* The upper or lower triangle of the Hermitian matrix A, packed */
/* columnwise in a linear array. The j-th column of A is stored */
/* in the array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* AFP (input) COMPLEX array, dimension (N*(N+1)/2) */
/* The triangular factor U or L from the Cholesky factorization */
/* A = U**H*U or A = L*L**H, as computed by SPPTRF/CPPTRF, */
/* packed columnwise in a linear array in the same format as A */
/* (see AP). */
/* B (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by CPPTRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* FERR (output) REAL array, dimension (NRHS) */
/* The estimated 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). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) REAL 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 array, dimension (2*N) */
/* RWORK (workspace) REAL array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Internal Parameters */
/* =================== */
/* ITMAX is the maximum number of steps of iterative refinement. */
/* ==================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
--afp;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < max(1,*n)) {
*info = -7;
} else if (*ldx < max(1,*n)) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPPRFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - A * X */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
q__1.r = -1.f, q__1.i = -0.f;
chpmv_(uplo, n, &q__1, &ap[1], &x[j * x_dim1 + 1], &c__1, &c_b1, &
work[1], &c__1);
/* Compute componentwise relative backward error from formula */
/* max(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. If the i-th component of the denominator is less */
/* than SAFE2, then SAFE1 is added to the i-th components of the */
/* numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
rwork[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[
i__ + j * b_dim1]), dabs(r__2));
/* L30: */
}
/* Compute abs(A)*abs(X) + abs(B). */
kk = 1;
if (upper) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[k + j
* x_dim1]), dabs(r__2));
ik = kk;
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = ik;
rwork[i__] += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[ik]), dabs(r__2))) * xk;
i__4 = ik;
i__5 = i__ + j * x_dim1;
s += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 = r_imag(&
ap[ik]), dabs(r__2))) * ((r__3 = x[i__5].r, dabs(
r__3)) + (r__4 = r_imag(&x[i__ + j * x_dim1]),
dabs(r__4)));
++ik;
/* L40: */
}
i__3 = kk + k - 1;
rwork[k] = rwork[k] + (r__1 = ap[i__3].r, dabs(r__1)) * xk +
s;
kk += k;
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[k + j
* x_dim1]), dabs(r__2));
i__3 = kk;
rwork[k] += (r__1 = ap[i__3].r, dabs(r__1)) * xk;
ik = kk + 1;
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = ik;
rwork[i__] += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[ik]), dabs(r__2))) * xk;
i__4 = ik;
i__5 = i__ + j * x_dim1;
s += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 = r_imag(&
ap[ik]), dabs(r__2))) * ((r__3 = x[i__5].r, dabs(
r__3)) + (r__4 = r_imag(&x[i__ + j * x_dim1]),
dabs(r__4)));
++ik;
/* L60: */
}
rwork[k] += s;
kk += *n - k + 1;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2))) / rwork[i__];
s = dmax(r__3,r__4);
} else {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + safe1) / (rwork[i__]
+ safe1);
s = dmax(r__3,r__4);
}
/* L80: */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if */
/* 1) The residual BERR(J) is larger than machine epsilon, and */
/* 2) BERR(J) decreased by at least a factor of 2 during the */
/* last iteration, and */
/* 3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
/* Update solution and try again. */
cpptrs_(uplo, n, &c__1, &afp[1], &work[1], n, info);
caxpy_(n, &c_b1, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
lstres = berr[j];
++count;
goto L20;
}
/* Bound error from formula */
/* norm(X - XTRUE) / norm(X) .le. FERR = */
/* norm( abs(inv(A))* */
/* ( abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) / norm(X) */
/* where */
/* norm(Z) is the magnitude of the largest component of Z */
/* inv(A) is the inverse of A */
/* abs(Z) is the componentwise absolute value of the matrix or */
/* vector Z */
/* NZ is the maximum number of nonzeros in any row of A, plus 1 */
/* EPS is machine epsilon */
/* The i-th component of abs(R)+NZ*EPS*(abs(A)*abs(X)+abs(B)) */
/* is incremented by SAFE1 if the i-th component of */
/* abs(A)*abs(X) + abs(B) is less than SAFE2. */
/* Use CLACN2 to estimate the infinity-norm of the matrix */
/* inv(A) * diag(W), */
/* where W = abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__];
} else {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
clacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(A'). */
cpptrs_(uplo, n, &c__1, &afp[1], &work[1], n, info)
;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L110: */
}
} else if (kase == 2) {
/* Multiply by inv(A)*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L120: */
}
cpptrs_(uplo, n, &c__1, &afp[1], &work[1], n, info)
;
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * x_dim1;
r__3 = lstres, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L130: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of CPPRFS */
} /* cpprfs_ */
/* Subroutine */ int cppsv_(char *uplo, integer *n, integer *nrhs, complex *
ap, complex *b, integer *ldb, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
CPPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**H* U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The number of linear equations, i.e., 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 matrix B. NRHS >= 0.
AP (input/output) COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H, in the same storage
format as A.
B (input/output) COMPLEX array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, 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.
Further Details
===============
The packed storage scheme is illustrated by the following example
when N = 4, UPLO = 'U':
Two-dimensional storage of the Hermitian matrix A:
a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = conjg(aji))
a44
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
=====================================================================
Test the input parameters.
Parameter adjustments */
/* System generated locals */
integer b_dim1, b_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *), cpptrf_(
char *, integer *, complex *, integer *), cpptrs_(char *,
integer *, integer *, complex *, complex *, integer *, integer *);
--ap;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
*info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < max(1,*n)) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPPSV ", &i__1);
return 0;
}
/* Compute the Cholesky factorization A = U'*U or A = L*L'. */
cpptrf_(uplo, n, &ap[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
cpptrs_(uplo, n, nrhs, &ap[1], &b[b_offset], ldb, info);
}
return 0;
/* End of CPPSV */
} /* cppsv_ */
/* Subroutine */ int cppsv_(char *uplo, integer *n, integer *nrhs, complex *
ap, complex *b, integer *ldb, integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, i__1;
/* Local variables */
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* CPPSV computes the solution to a complex system of linear equations */
/* A * X = B, */
/* where A is an N-by-N Hermitian positive definite matrix stored in */
/* packed format and X and B are N-by-NRHS matrices. */
/* The Cholesky decomposition is used to factor A as */
/* A = U**H* U, if UPLO = 'U', or */
/* A = L * L**H, if UPLO = 'L', */
/* where U is an upper triangular matrix and L is a lower triangular */
/* matrix. The factored form of A is then used to solve the system of */
/* equations A * X = B. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The number of linear equations, i.e., 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 matrix B. NRHS >= 0. */
/* AP (input/output) COMPLEX array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangle of the Hermitian matrix */
/* A, packed columnwise in a linear array. The j-th column of A */
/* is stored in the array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* See below for further details. */
/* On exit, if INFO = 0, the factor U or L from the Cholesky */
/* factorization A = U**H*U or A = L*L**H, in the same storage */
/* format as A. */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS right hand side matrix B. */
/* On exit, if INFO = 0, the N-by-NRHS solution matrix X. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, 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. */
/* Further Details */
/* =============== */
/* The packed storage scheme is illustrated by the following example */
/* when N = 4, UPLO = 'U': */
/* Two-dimensional storage of the Hermitian matrix A: */
/* a11 a12 a13 a14 */
/* a22 a23 a24 */
/* a33 a34 (aij = conjg(aji)) */
/* a44 */
/* Packed storage of the upper triangle of A: */
/* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < max(1,*n)) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPPSV ", &i__1);
return 0;
}
/* Compute the Cholesky factorization A = U'*U or A = L*L'. */
cpptrf_(uplo, n, &ap[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
cpptrs_(uplo, n, nrhs, &ap[1], &b[b_offset], ldb, info);
}
return 0;
/* End of CPPSV */
} /* cppsv_ */
int main(void)
{
/* Local scalars */
char uplo, uplo_i;
lapack_int n, n_i;
lapack_int nrhs, nrhs_i;
lapack_int ldb, ldb_i;
lapack_int ldb_r;
lapack_int info, info_i;
lapack_int i;
int failed;
/* Local arrays */
lapack_complex_float *ap = NULL, *ap_i = NULL;
lapack_complex_float *b = NULL, *b_i = NULL;
lapack_complex_float *b_save = NULL;
lapack_complex_float *ap_r = NULL;
lapack_complex_float *b_r = NULL;
/* Iniitialize the scalar parameters */
init_scalars_cpptrs( &uplo, &n, &nrhs, &ldb );
ldb_r = nrhs+2;
uplo_i = uplo;
n_i = n;
nrhs_i = nrhs;
ldb_i = ldb;
/* Allocate memory for the LAPACK routine arrays */
ap = (lapack_complex_float *)
LAPACKE_malloc( ((n*(n+1)/2)) * sizeof(lapack_complex_float) );
b = (lapack_complex_float *)
LAPACKE_malloc( ldb*nrhs * sizeof(lapack_complex_float) );
/* Allocate memory for the C interface function arrays */
ap_i = (lapack_complex_float *)
LAPACKE_malloc( ((n*(n+1)/2)) * sizeof(lapack_complex_float) );
b_i = (lapack_complex_float *)
LAPACKE_malloc( ldb*nrhs * sizeof(lapack_complex_float) );
/* Allocate memory for the backup arrays */
b_save = (lapack_complex_float *)
LAPACKE_malloc( ldb*nrhs * sizeof(lapack_complex_float) );
/* Allocate memory for the row-major arrays */
ap_r = (lapack_complex_float *)
LAPACKE_malloc( n*(n+1)/2 * sizeof(lapack_complex_float) );
b_r = (lapack_complex_float *)
LAPACKE_malloc( n*(nrhs+2) * sizeof(lapack_complex_float) );
/* Initialize input arrays */
init_ap( (n*(n+1)/2), ap );
init_b( ldb*nrhs, b );
/* Backup the ouptut arrays */
for( i = 0; i < ldb*nrhs; i++ ) {
b_save[i] = b[i];
}
/* Call the LAPACK routine */
cpptrs_( &uplo, &n, &nrhs, ap, b, &ldb, &info );
/* Initialize input data, call the column-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < (n*(n+1)/2); i++ ) {
ap_i[i] = ap[i];
}
for( i = 0; i < ldb*nrhs; i++ ) {
b_i[i] = b_save[i];
}
info_i = LAPACKE_cpptrs_work( LAPACK_COL_MAJOR, uplo_i, n_i, nrhs_i, ap_i,
b_i, ldb_i );
failed = compare_cpptrs( b, b_i, info, info_i, ldb, nrhs );
if( failed == 0 ) {
printf( "PASSED: column-major middle-level interface to cpptrs\n" );
} else {
printf( "FAILED: column-major middle-level interface to cpptrs\n" );
}
/* Initialize input data, call the column-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < (n*(n+1)/2); i++ ) {
ap_i[i] = ap[i];
}
for( i = 0; i < ldb*nrhs; i++ ) {
b_i[i] = b_save[i];
}
info_i = LAPACKE_cpptrs( LAPACK_COL_MAJOR, uplo_i, n_i, nrhs_i, ap_i, b_i,
ldb_i );
failed = compare_cpptrs( b, b_i, info, info_i, ldb, nrhs );
if( failed == 0 ) {
printf( "PASSED: column-major high-level interface to cpptrs\n" );
} else {
printf( "FAILED: column-major high-level interface to cpptrs\n" );
}
/* Initialize input data, call the row-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < (n*(n+1)/2); i++ ) {
ap_i[i] = ap[i];
}
for( i = 0; i < ldb*nrhs; i++ ) {
b_i[i] = b_save[i];
}
LAPACKE_cpp_trans( LAPACK_COL_MAJOR, uplo, n, ap_i, ap_r );
LAPACKE_cge_trans( LAPACK_COL_MAJOR, n, nrhs, b_i, ldb, b_r, nrhs+2 );
info_i = LAPACKE_cpptrs_work( LAPACK_ROW_MAJOR, uplo_i, n_i, nrhs_i, ap_r,
b_r, ldb_r );
LAPACKE_cge_trans( LAPACK_ROW_MAJOR, n, nrhs, b_r, nrhs+2, b_i, ldb );
failed = compare_cpptrs( b, b_i, info, info_i, ldb, nrhs );
if( failed == 0 ) {
printf( "PASSED: row-major middle-level interface to cpptrs\n" );
} else {
printf( "FAILED: row-major middle-level interface to cpptrs\n" );
}
/* Initialize input data, call the row-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < (n*(n+1)/2); i++ ) {
ap_i[i] = ap[i];
}
for( i = 0; i < ldb*nrhs; i++ ) {
b_i[i] = b_save[i];
}
/* Init row_major arrays */
LAPACKE_cpp_trans( LAPACK_COL_MAJOR, uplo, n, ap_i, ap_r );
LAPACKE_cge_trans( LAPACK_COL_MAJOR, n, nrhs, b_i, ldb, b_r, nrhs+2 );
info_i = LAPACKE_cpptrs( LAPACK_ROW_MAJOR, uplo_i, n_i, nrhs_i, ap_r, b_r,
ldb_r );
LAPACKE_cge_trans( LAPACK_ROW_MAJOR, n, nrhs, b_r, nrhs+2, b_i, ldb );
failed = compare_cpptrs( b, b_i, info, info_i, ldb, nrhs );
if( failed == 0 ) {
printf( "PASSED: row-major high-level interface to cpptrs\n" );
} else {
printf( "FAILED: row-major high-level interface to cpptrs\n" );
}
/* Release memory */
if( ap != NULL ) {
LAPACKE_free( ap );
}
if( ap_i != NULL ) {
LAPACKE_free( ap_i );
}
if( ap_r != NULL ) {
LAPACKE_free( ap_r );
}
if( b != NULL ) {
LAPACKE_free( b );
}
if( b_i != NULL ) {
LAPACKE_free( b_i );
}
if( b_r != NULL ) {
LAPACKE_free( b_r );
}
if( b_save != NULL ) {
LAPACKE_free( b_save );
}
return 0;
}
