DLLEXPORT MKL_INT z_cholesky_solve_factored(MKL_INT n, MKL_INT nrhs, MKL_Complex16 a[], MKL_Complex16 b[])
{
char uplo = 'L';
MKL_INT info = 0;
zpotrs_(&uplo, &n, &nrhs, a, &n, b, &n, &info);
return info;
}
DLLEXPORT int z_cholesky_solve_factored(int n, int nrhs, doublecomplex a[], doublecomplex b[])
{
char uplo = 'L';
int info = 0;
zpotrs_(&uplo, &n, &nrhs, a, &n, b, &n, &info);
return info;
}
DLLEXPORT int z_cholesky_solve(int n, int nrhs, doublecomplex a[], doublecomplex b[])
{
doublecomplex* clone = new doublecomplex[n*n];
memcpy(clone, a, n*n*sizeof(doublecomplex));
char uplo = 'L';
int info = 0;
zpotrf_(&uplo, &n, clone, &n, &info);
if (info != 0){
delete[] clone;
return info;
}
zpotrs_(&uplo, &n, &nrhs, clone, &n, b, &n, &info);
return info;
}
DLLEXPORT MKL_INT z_cholesky_solve(MKL_INT n, MKL_INT nrhs, MKL_Complex16 a[], MKL_Complex16 b[])
{
MKL_Complex16* clone = new MKL_Complex16[n*n];
std::memcpy(clone, a, n*n*sizeof(MKL_Complex16));
char uplo = 'L';
MKL_INT info = 0;
zpotrf_(&uplo, &n, clone, &n, &info);
if (info != 0){
delete[] clone;
return info;
}
zpotrs_(&uplo, &n, &nrhs, clone, &n, b, &n, &info);
delete[] clone;
return info;
}
/* Subroutine */ int zposv_(char *uplo, integer *n, integer *nrhs,
doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb,
integer *info, ftnlen uplo_len)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), zpotrf_(
char *, integer *, doublecomplex *, integer *, integer *, ftnlen),
zpotrs_(char *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *, ftnlen);
/* -- 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 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZPOSV computes the solution to a complex system of linear equations */
/* A * X = B, */
/* where A is an N-by-N Hermitian positive definite matrix 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. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the Hermitian matrix A. If UPLO = 'U', the leading */
/* N-by-N upper triangular part of A contains the upper */
/* triangular part of the matrix A, and the strictly lower */
/* triangular part of A is not referenced. If UPLO = 'L', the */
/* leading N-by-N lower triangular part of A contains the lower */
/* triangular part of the matrix A, and the strictly upper */
/* triangular part of A is not referenced. */
/* On exit, if INFO = 0, the factor U or L from the Cholesky */
/* factorization A = U**H*U or A = L*L**H. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (input/output) COMPLEX*16 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. */
/* ===================================================================== */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
ftnlen)1, (ftnlen)1)) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPOSV ", &i__1, (ftnlen)6);
return 0;
}
/* Compute the Cholesky factorization A = U'*U or A = L*L'. */
zpotrf_(uplo, n, &a[a_offset], lda, info, (ftnlen)1);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
zpotrs_(uplo, n, nrhs, &a[a_offset], lda, &b[b_offset], ldb, info, (
ftnlen)1);
}
return 0;
/* End of ZPOSV */
} /* zposv_ */
/* Subroutine */ int zerrpo_(char *path, integer *nunit)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
doublecomplex z__1;
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
doublecomplex a[16] /* was [4][4] */, b[4];
integer i__, j;
doublereal r__[4];
doublecomplex w[8], x[4];
char c2[2];
doublereal r1[4], r2[4];
doublecomplex af[16] /* was [4][4] */;
integer info;
doublereal anrm, rcond;
extern /* Subroutine */ int zpbtf2_(char *, integer *, integer *,
doublecomplex *, integer *, integer *), zpotf2_(char *,
integer *, doublecomplex *, integer *, integer *),
alaesm_(char *, logical *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), zpbcon_(char *, integer *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *), zpbequ_(char *,
integer *, integer *, doublecomplex *, integer *, doublereal *,
doublereal *, doublereal *, integer *), zpbrfs_(char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *), zpbtrf_(char *,
integer *, integer *, doublecomplex *, integer *, integer *), zpocon_(char *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zppcon_(char *, integer *, doublecomplex *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zpoequ_(integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublereal *, integer *), zpbtrs_(
char *, integer *, integer *, integer *, doublecomplex *, integer
*, doublecomplex *, integer *, integer *), zporfs_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *
, integer *, doublecomplex *, integer *, doublecomplex *, integer
*, doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zpotrf_(char *, integer *, doublecomplex *,
integer *, integer *), zpotri_(char *, integer *,
doublecomplex *, integer *, integer *), zppequ_(char *,
integer *, doublecomplex *, doublereal *, doublereal *,
doublereal *, integer *), zpprfs_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *), zpptrf_(char *
, integer *, doublecomplex *, integer *), zpptri_(char *,
integer *, doublecomplex *, integer *), zpotrs_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *), zpptrs_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *);
/* 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 */
/* ======= */
/* ZERRPO tests the error exits for the COMPLEX*16 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;
d__1 = 1. / (doublereal) (i__ + j);
d__2 = -1. / (doublereal) (i__ + j);
z__1.r = d__1, z__1.i = d__2;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = i__ + (j << 2) - 5;
d__1 = 1. / (doublereal) (i__ + j);
d__2 = -1. / (doublereal) (i__ + j);
z__1.r = d__1, z__1.i = d__2;
af[i__1].r = z__1.r, af[i__1].i = z__1.i;
/* L10: */
}
i__1 = j - 1;
b[i__1].r = 0., b[i__1].i = 0.;
r1[j - 1] = 0.;
r2[j - 1] = 0.;
i__1 = j - 1;
w[i__1].r = 0., w[i__1].i = 0.;
i__1 = j - 1;
x[i__1].r = 0., x[i__1].i = 0.;
/* L20: */
}
anrm = 1.;
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")) {
/* ZPOTRF */
s_copy(srnamc_1.srnamt, "ZPOTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpotrf_("/", &c__0, a, &c__1, &info);
chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpotrf_("U", &c_n1, a, &c__1, &info);
chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zpotrf_("U", &c__2, a, &c__1, &info);
chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPOTF2 */
s_copy(srnamc_1.srnamt, "ZPOTF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpotf2_("/", &c__0, a, &c__1, &info);
chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpotf2_("U", &c_n1, a, &c__1, &info);
chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zpotf2_("U", &c__2, a, &c__1, &info);
chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPOTRI */
s_copy(srnamc_1.srnamt, "ZPOTRI", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpotri_("/", &c__0, a, &c__1, &info);
chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpotri_("U", &c_n1, a, &c__1, &info);
chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zpotri_("U", &c__2, a, &c__1, &info);
chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPOTRS */
s_copy(srnamc_1.srnamt, "ZPOTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpotrs_("/", &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpotrs_("U", &c_n1, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpotrs_("U", &c__0, &c_n1, a, &c__1, b, &c__1, &info);
chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zpotrs_("U", &c__2, &c__1, a, &c__1, b, &c__2, &info);
chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zpotrs_("U", &c__2, &c__1, a, &c__2, b, &c__1, &info);
chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPORFS */
s_copy(srnamc_1.srnamt, "ZPORFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zporfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zporfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zporfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zporfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &c__2,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &c__2,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__1, x, &c__2,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__2, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPOCON */
s_copy(srnamc_1.srnamt, "ZPOCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpocon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpocon_("U", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zpocon_("U", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
d__1 = -anrm;
zpocon_("U", &c__1, a, &c__1, &d__1, &rcond, w, r__, &info)
;
chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPOEQU */
s_copy(srnamc_1.srnamt, "ZPOEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpoequ_(&c_n1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpoequ_(&c__2, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("ZPOEQU", &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")) {
/* ZPPTRF */
s_copy(srnamc_1.srnamt, "ZPPTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpptrf_("/", &c__0, a, &info);
chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpptrf_("U", &c_n1, a, &info);
chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPPTRI */
s_copy(srnamc_1.srnamt, "ZPPTRI", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpptri_("/", &c__0, a, &info);
chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpptri_("U", &c_n1, a, &info);
chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPPTRS */
s_copy(srnamc_1.srnamt, "ZPPTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpptrs_("/", &c__0, &c__0, a, b, &c__1, &info);
chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpptrs_("U", &c_n1, &c__0, a, b, &c__1, &info);
chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpptrs_("U", &c__0, &c_n1, a, b, &c__1, &info);
chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zpptrs_("U", &c__2, &c__1, a, b, &c__1, &info);
chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPPRFS */
s_copy(srnamc_1.srnamt, "ZPPRFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpprfs_("/", &c__0, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpprfs_("U", &c_n1, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpprfs_("U", &c__0, &c_n1, a, af, b, &c__1, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zpprfs_("U", &c__2, &c__1, a, af, b, &c__1, x, &c__2, r1, r2, w, r__,
&info);
chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
zpprfs_("U", &c__2, &c__1, a, af, b, &c__2, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPPCON */
s_copy(srnamc_1.srnamt, "ZPPCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zppcon_("/", &c__0, a, &anrm, &rcond, w, r__, &info);
chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zppcon_("U", &c_n1, a, &anrm, &rcond, w, r__, &info);
chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
d__1 = -anrm;
zppcon_("U", &c__1, a, &d__1, &rcond, w, r__, &info);
chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPPEQU */
s_copy(srnamc_1.srnamt, "ZPPEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zppequ_("/", &c__0, a, r1, &rcond, &anrm, &info);
chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zppequ_("U", &c_n1, a, r1, &rcond, &anrm, &info);
chkxer_("ZPPEQU", &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")) {
/* ZPBTRF */
s_copy(srnamc_1.srnamt, "ZPBTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpbtrf_("/", &c__0, &c__0, a, &c__1, &info);
chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpbtrf_("U", &c_n1, &c__0, a, &c__1, &info);
chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpbtrf_("U", &c__1, &c_n1, a, &c__1, &info);
chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zpbtrf_("U", &c__2, &c__1, a, &c__1, &info);
chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPBTF2 */
s_copy(srnamc_1.srnamt, "ZPBTF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpbtf2_("/", &c__0, &c__0, a, &c__1, &info);
chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpbtf2_("U", &c_n1, &c__0, a, &c__1, &info);
chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpbtf2_("U", &c__1, &c_n1, a, &c__1, &info);
chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zpbtf2_("U", &c__2, &c__1, a, &c__1, &info);
chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPBTRS */
s_copy(srnamc_1.srnamt, "ZPBTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpbtrs_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpbtrs_("U", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpbtrs_("U", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zpbtrs_("U", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, &info);
chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zpbtrs_("U", &c__2, &c__1, &c__1, a, &c__1, b, &c__1, &info);
chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zpbtrs_("U", &c__2, &c__0, &c__1, a, &c__1, b, &c__1, &info);
chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPBRFS */
s_copy(srnamc_1.srnamt, "ZPBRFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpbrfs_("/", &c__0, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPBCON */
s_copy(srnamc_1.srnamt, "ZPBCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpbcon_("/", &c__0, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpbcon_("U", &c_n1, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpbcon_("U", &c__1, &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zpbcon_("U", &c__2, &c__1, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
d__1 = -anrm;
zpbcon_("U", &c__1, &c__0, a, &c__1, &d__1, &rcond, w, r__, &info);
chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPBEQU */
s_copy(srnamc_1.srnamt, "ZPBEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpbequ_("/", &c__0, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpbequ_("U", &c_n1, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpbequ_("U", &c__1, &c_n1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zpbequ_("U", &c__2, &c__1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("ZPBEQU", &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 ZERRPO */
} /* zerrpo_ */
/* Subroutine */
int zposvx_(char *fact, char *uplo, integer *n, integer * nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * ldaf, char *equed, doublereal *s, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal *rwork, integer * info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2;
doublecomplex z__1;
/* Local variables */
integer i__, j;
doublereal amax, smin, smax;
extern logical lsame_(char *, char *);
doublereal scond, anorm;
logical equil, rcequ;
extern doublereal dlamch_(char *);
logical nofact;
extern /* Subroutine */
int xerbla_(char *, integer *);
doublereal bignum;
extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *);
extern /* Subroutine */
int zlaqhe_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, char *);
integer infequ;
extern /* Subroutine */
int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zpocon_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *) ;
doublereal smlnum;
extern /* Subroutine */
int zpoequ_(integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, integer *), zporfs_( char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpotrf_(char *, integer *, doublecomplex *, integer *, integer *), zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *);
/* -- LAPACK driver 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 Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--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 = dlamch_("Safe minimum");
bignum = 1. / 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 (*lda < max(1,*n))
{
*info = -6;
}
else if (*ldaf < max(1,*n))
{
*info = -8;
}
else if (lsame_(fact, "F") && ! (rcequ || lsame_( equed, "N")))
{
*info = -9;
}
else
{
if (rcequ)
{
smin = bignum;
smax = 0.;
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
/* Computing MIN */
d__1 = smin;
d__2 = s[j]; // , expr subst
smin = min(d__1,d__2);
/* Computing MAX */
d__1 = smax;
d__2 = s[j]; // , expr subst
smax = max(d__1,d__2);
/* L10: */
}
if (smin <= 0.)
{
*info = -10;
}
else if (*n > 0)
{
scond = max(smin,smlnum) / min(smax,bignum);
}
else
{
scond = 1.;
}
}
if (*info == 0)
{
if (*ldb < max(1,*n))
{
*info = -12;
}
else if (*ldx < max(1,*n))
{
*info = -14;
}
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("ZPOSVX", &i__1);
return 0;
}
if (equil)
{
/* Compute row and column scalings to equilibrate the matrix A. */
zpoequ_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ);
if (infequ == 0)
{
/* Equilibrate the matrix. */
zlaqhe_(uplo, n, &a[a_offset], lda, &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;
z__1.r = s[i__4] * b[i__5].r;
z__1.i = s[i__4] * b[i__5].i; // , expr subst
b[i__3].r = z__1.r;
b[i__3].i = z__1.i; // , expr subst
/* L20: */
}
/* L30: */
}
}
if (nofact || equil)
{
/* Compute the Cholesky factorization A = U**H *U or A = L*L**H. */
zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
zpotrf_(uplo, n, &af[af_offset], ldaf, info);
/* Return if INFO is non-zero. */
if (*info > 0)
{
*rcond = 0.;
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = zlanhe_("1", uplo, n, &a[a_offset], lda, &rwork[1]);
/* Compute the reciprocal of the condition number of A. */
zpocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1], info);
/* Compute the solution matrix X. */
zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
zpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
zporfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &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;
z__1.r = s[i__4] * x[i__5].r;
z__1.i = s[i__4] * x[i__5].i; // , expr subst
x[i__3].r = z__1.r;
x[i__3].i = z__1.i; // , expr subst
/* L40: */
}
/* L50: */
}
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
ferr[j] /= scond;
/* L60: */
}
}
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < dlamch_("Epsilon"))
{
*info = *n + 1;
}
return 0;
/* End of ZPOSVX */
}
/* Subroutine */ int zposvx_(char *fact, char *uplo, integer *n, integer *
nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *
ldaf, char *equed, doublereal *s, doublecomplex *b, integer *ldb,
doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr,
doublereal *berr, doublecomplex *work, doublereal *rwork, integer *
info, ftnlen fact_len, ftnlen uplo_len, ftnlen equed_len)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2;
doublecomplex z__1;
/* Local variables */
static integer i__, j;
static doublereal amax, smin, smax;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
static doublereal scond, anorm;
static logical equil, rcequ;
extern doublereal dlamch_(char *, ftnlen);
static logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
static doublereal bignum;
extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *,
integer *, doublereal *, ftnlen, ftnlen);
extern /* Subroutine */ int zlaqhe_(char *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublereal *, char *,
ftnlen, ftnlen);
static integer infequ;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, ftnlen),
zpocon_(char *, integer *, doublecomplex *, integer *, doublereal
*, doublereal *, doublecomplex *, doublereal *, integer *, ftnlen)
;
static doublereal smlnum;
extern /* Subroutine */ int zpoequ_(integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublereal *, integer *), zporfs_(
char *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *, ftnlen), zpotrf_(char *,
integer *, doublecomplex *, integer *, integer *, ftnlen),
zpotrs_(char *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *, ftnlen);
/* -- LAPACK driver routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZPOSVX 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 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**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. */
/* 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, AF contains the factored form of A. */
/* If EQUED = 'Y', the matrix A has been equilibrated */
/* with scaling factors given by S. A and AF will not */
/* be modified. */
/* = 'N': The matrix A will be copied to AF and factored. */
/* = 'E': The matrix A will be equilibrated if necessary, then */
/* copied to AF 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. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the Hermitian matrix A, except if FACT = 'F' and */
/* EQUED = 'Y', then A must contain the equilibrated matrix */
/* diag(S)*A*diag(S). If UPLO = 'U', the leading */
/* N-by-N upper triangular part of A contains the upper */
/* triangular part of the matrix A, and the strictly lower */
/* triangular part of A is not referenced. If UPLO = 'L', the */
/* leading N-by-N lower triangular part of A contains the lower */
/* triangular part of the matrix A, and the strictly upper */
/* triangular part of A is not referenced. 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). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input or output) COMPLEX*16 array, dimension (LDAF,N) */
/* If FACT = 'F', then AF 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 AF is the factored form */
/* of the equilibrated matrix diag(S)*A*diag(S). */
/* If FACT = 'N', then AF 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 AF 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 A for the form of the */
/* equilibrated matrix). */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* 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) DOUBLE PRECISION 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*16 array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS righthand 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*16 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) DOUBLE PRECISION */
/* 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) DOUBLE PRECISION 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) 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 (2*N) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 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. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--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", (ftnlen)1, (ftnlen)1);
equil = lsame_(fact, "E", (ftnlen)1, (ftnlen)1);
if (nofact || equil) {
*(unsigned char *)equed = 'N';
rcequ = FALSE_;
} else {
rcequ = lsame_(equed, "Y", (ftnlen)1, (ftnlen)1);
smlnum = dlamch_("Safe minimum", (ftnlen)12);
bignum = 1. / smlnum;
}
/* Test the input parameters. */
if (! nofact && ! equil && ! lsame_(fact, "F", (ftnlen)1, (ftnlen)1)) {
*info = -1;
} else if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo,
"L", (ftnlen)1, (ftnlen)1)) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else if (*ldaf < max(1,*n)) {
*info = -8;
} else if (lsame_(fact, "F", (ftnlen)1, (ftnlen)1) && ! (rcequ || lsame_(
equed, "N", (ftnlen)1, (ftnlen)1))) {
*info = -9;
} else {
if (rcequ) {
smin = bignum;
smax = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
d__1 = smin, d__2 = s[j];
smin = min(d__1,d__2);
/* Computing MAX */
d__1 = smax, d__2 = s[j];
smax = max(d__1,d__2);
/* L10: */
}
if (smin <= 0.) {
*info = -10;
} else if (*n > 0) {
scond = max(smin,smlnum) / min(smax,bignum);
} else {
scond = 1.;
}
}
if (*info == 0) {
if (*ldb < max(1,*n)) {
*info = -12;
} else if (*ldx < max(1,*n)) {
*info = -14;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPOSVX", &i__1, (ftnlen)6);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
zpoequ_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
zlaqhe_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed, (
ftnlen)1, (ftnlen)1);
rcequ = lsame_(equed, "Y", (ftnlen)1, (ftnlen)1);
}
}
/* 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;
z__1.r = s[i__4] * b[i__5].r, z__1.i = s[i__4] * b[i__5].i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L20: */
}
/* L30: */
}
}
if (nofact || equil) {
/* Compute the Cholesky factorization A = U'*U or A = L*L'. */
zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf, (ftnlen)
1);
zpotrf_(uplo, n, &af[af_offset], ldaf, info, (ftnlen)1);
/* Return if INFO is non-zero. */
if (*info != 0) {
if (*info > 0) {
*rcond = 0.;
}
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = zlanhe_("1", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, (
ftnlen)1);
/* Compute the reciprocal of the condition number of A. */
zpocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1],
info, (ftnlen)1);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < dlamch_("Epsilon", (ftnlen)7)) {
*info = *n + 1;
}
/* Compute the solution matrix X. */
zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx, (ftnlen)4);
zpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info, (
ftnlen)1);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
zporfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &b[
b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1], &
rwork[1], info, (ftnlen)1);
/* 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;
z__1.r = s[i__4] * x[i__5].r, z__1.i = s[i__4] * x[i__5].i;
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
/* L40: */
}
/* L50: */
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] /= scond;
/* L60: */
}
}
return 0;
/* End of ZPOSVX */
} /* zposvx_ */
/* Subroutine */
int zposvxx_(char *fact, char *uplo, integer *n, integer * nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * ldaf, char *equed, doublereal *s, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *rpvgrw, 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 a_dim1, a_offset, af_dim1, af_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;
/* Local variables */
integer j;
doublereal amax, smin, smax;
extern doublereal zla_porpvgrw_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *);
extern logical lsame_(char *, char *);
doublereal scond;
logical equil, rcequ;
extern doublereal dlamch_(char *);
logical nofact;
extern /* Subroutine */
int xerbla_(char *, integer *);
doublereal bignum;
extern /* Subroutine */
int zlaqhe_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, char *);
integer infequ;
extern /* Subroutine */
int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *);
doublereal smlnum;
extern /* Subroutine */
int zpotrf_(char *, integer *, doublecomplex *, integer *, integer *), zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *), zlascl2_(integer *, integer *, doublereal *, doublecomplex *, integer *), zpoequb_(integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, integer *), zporfsx_(char *, char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublecomplex *, doublereal *, integer * );
/* -- LAPACK driver 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 Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* 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;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--s;
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;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
smlnum = dlamch_("Safe minimum");
bignum = 1. / smlnum;
if (nofact || equil)
{
*(unsigned char *)equed = 'N';
rcequ = FALSE_;
}
else
{
rcequ = lsame_(equed, "Y");
}
/* Default is failure. If an input parameter is wrong or */
/* factorization fails, make everything look horrible. Only the */
/* pivot growth is set here, the rest is initialized in ZPORFSX. */
*rpvgrw = 0.;
/* Test the input parameters. PARAMS is not tested until ZPORFSX. */
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 (*lda < max(1,*n))
{
*info = -6;
}
else if (*ldaf < max(1,*n))
{
*info = -8;
}
else if (lsame_(fact, "F") && ! (rcequ || lsame_( equed, "N")))
{
*info = -9;
}
else
{
if (rcequ)
{
smin = bignum;
smax = 0.;
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
/* Computing MIN */
d__1 = smin;
d__2 = s[j]; // , expr subst
smin = min(d__1,d__2);
/* Computing MAX */
d__1 = smax;
d__2 = s[j]; // , expr subst
smax = max(d__1,d__2);
/* L10: */
}
if (smin <= 0.)
{
*info = -10;
}
else if (*n > 0)
{
scond = max(smin,smlnum) / min(smax,bignum);
}
else
{
scond = 1.;
}
}
if (*info == 0)
{
if (*ldb < max(1,*n))
{
*info = -12;
}
else if (*ldx < max(1,*n))
{
*info = -14;
}
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("ZPOSVXX", &i__1);
return 0;
}
if (equil)
{
/* Compute row and column scalings to equilibrate the matrix A. */
zpoequb_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ);
if (infequ == 0)
{
/* Equilibrate the matrix. */
zlaqhe_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed);
rcequ = lsame_(equed, "Y");
}
}
/* Scale the right-hand side. */
if (rcequ)
{
zlascl2_(n, nrhs, &s[1], &b[b_offset], ldb);
}
if (nofact || equil)
{
/* Compute the Cholesky factorization of A. */
zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
zpotrf_(uplo, n, &af[af_offset], ldaf, info);
/* Return if INFO is non-zero. */
if (*info > 0)
{
/* Pivot in column INFO is exactly 0 */
/* Compute the reciprocal pivot growth factor of the */
/* leading rank-deficient INFO columns of A. */
*rpvgrw = zla_porpvgrw_(uplo, n, &a[a_offset], lda, &af[ af_offset], ldaf, &rwork[1]);
return 0;
}
}
/* Compute the reciprocal pivot growth factor RPVGRW. */
*rpvgrw = zla_porpvgrw_(uplo, n, &a[a_offset], lda, &af[af_offset], ldaf, &rwork[1]);
/* Compute the solution matrix X. */
zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
zpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
zporfsx_(uplo, equed, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, & s[1], &b[b_offset], ldb, &x[x_offset], ldx, rcond, &berr[1], n_err_bnds__, &err_bnds_norm__[err_bnds_norm_offset], & err_bnds_comp__[err_bnds_comp_offset], nparams, ¶ms[1], &work[ 1], &rwork[1], info);
/* Scale solutions. */
if (rcequ)
{
zlascl2_(n, nrhs, &s[1], &x[x_offset], ldx);
}
return 0;
/* End of ZPOSVXX */
}
/* dest <- dest + sum_i eigVec[i]*H^{-1}*eigVec[i].resid,
resid = src - (-Dslash^2 + 4*mass^2)*dest
*/
static void initCG(su3_vector *src, su3_vector *dest, int Nvecs_curr, int Nvecs_max,
su3_vector **eigVec, double_complex *H, Real mass, int parity,
imp_ferm_links_t *fn){
/* Constants */
int ione = 1;
int otherparity = (parity == EVEN) ? ODD : EVEN;
Real msq_x4 = 4.0*mass*mass;
double dzero = (double)0.0;
double_complex zzero = dcmplx(dzero, dzero);
register int i;
int j, info;
double_complex cc;
double_complex *c, *H2;
su3_vector *resid;
c = (double_complex *)malloc(Nvecs_curr*sizeof(double_complex));
resid = (su3_vector *)malloc(sites_on_node*sizeof(su3_vector));
/* resid <- src - (-Dslash^2 + 4*mass^2)*dest */
dslash_fn_field(dest, resid, otherparity, fn);
dslash_fn_field(resid, resid, parity, fn);
FORSOMEFIELDPARITY_OMP(i, parity, default(shared)){
scalar_mult_sum_su3_vector(resid+i, dest+i, -msq_x4);
add_su3_vector(resid+i, src+i, resid+i);
} END_LOOP_OMP
/* c[i] = eigVec[i].resid */
for(j = 0; j < Nvecs_curr; j++){
// c[j] = zzero;
// FORSOMEFIELDPARITY_OMP(i, parity, private(cc) reduction(+:c[j])){
// cc = su3_dot(eigVec[j]+i, resid+i);
// CSUM(c[j], cc);
// } END_LOOP_OMP
double cctotr=0., cctoti=0.;
FORSOMEFIELDPARITY_OMP(i, parity, private(cc) reduction(+:cctotr,cctoti)){
cc = su3_dot(eigVec[j]+i, resid+i);
cctotr += cc.real;
cctoti += cc.imag;
} END_LOOP_OMP;
c[j].real = cctotr;
c[j].imag = cctoti;
}
g_vecdcomplexsum(c, Nvecs_curr);
free(resid);
H2 = (double_complex *)malloc(Nvecs_curr*Nvecs_curr*sizeof(double_complex));
/* H2 = H + 4*mass^2*I */
for(j = 0; j < Nvecs_curr; j++){
zcopy_(&Nvecs_curr, H+Nvecs_max*j, &ione, H2+Nvecs_curr*j, &ione);
CSUM(H2[(Nvecs_curr+1)*j], dcmplx(msq_x4, dzero));
}
/* Compute H^{-1}*c = H^{-1}*eigVec.resid with Cholesky decomposition */
zpotrf_("U", &Nvecs_curr, H2, &Nvecs_curr, &info);
zpotrs_("U", &Nvecs_curr, &ione, H2, &Nvecs_curr, c, &Nvecs_curr, &info);
free(H2);
/* dest <- dest + sum_j c[i]*eigVec[i] = dest + sum_i eigVec[i]*H^{-1}*eigVec[i].resid */
for(j = 0; j < Nvecs_curr; j++){
FORSOMEFIELDPARITY_OMP(i, parity, default(shared)){
c_scalar_mult_add_su3vec(dest+i, c+j, eigVec[j]+i);
} END_LOOP_OMP
}
free(c);
}
doublereal zla_porcond_c__(char *uplo, integer *n, doublecomplex *a, integer *
lda, doublecomplex *af, integer *ldaf, doublereal *c__, logical *
capply, integer *info, doublecomplex *work, doublereal *rwork, ftnlen
uplo_len)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, i__1, i__2, i__3, i__4;
doublereal ret_val, d__1, d__2;
doublecomplex z__1;
/* Local variables */
integer i__, j;
logical up;
doublereal tmp;
integer kase;
integer isave[3];
doublereal anorm;
doublereal ainvnm;
/* -- 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. -- */
/* Purpose */
/* ======= */
/* ZLA_PORCOND_C Computes the infinity norm condition number of */
/* op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector */
/* 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. */
/* A (input) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input) COMPLEX*16 array, dimension (LDAF,N) */
/* The triangular factor U or L from the Cholesky factorization */
/* A = U**T*U or A = L*L**T, as computed by ZPOTRF. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* C (input) DOUBLE PRECISION array, dimension (N) */
/* The vector C in the formula op(A) * inv(diag(C)). */
/* CAPPLY (input) LOGICAL */
/* If .TRUE. then access the vector C in the formula above. */
/* INFO (output) INTEGER */
/* = 0: Successful exit. */
/* i > 0: The ith argument is invalid. */
/* WORK (input) COMPLEX*16 array, dimension (2*N). */
/* Workspace. */
/* RWORK (input) DOUBLE PRECISION array, dimension (N). */
/* Workspace. */
/* ===================================================================== */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--c__;
--work;
--rwork;
/* Function Body */
ret_val = 0.;
*info = 0;
if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZLA_PORCOND_C", &i__1);
return ret_val;
}
up = FALSE_;
if (lsame_(uplo, "U")) {
up = TRUE_;
}
/* Compute norm of op(A)*op2(C). */
anorm = 0.;
if (up) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tmp = 0.;
if (*capply) {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
i__3 = j + i__ * a_dim1;
tmp += ((d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[
j + i__ * a_dim1]), abs(d__2))) / c__[j];
}
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
i__3 = i__ + j * a_dim1;
tmp += ((d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[
i__ + j * a_dim1]), abs(d__2))) / c__[j];
}
} else {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
i__3 = j + i__ * a_dim1;
tmp += (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[
j + i__ * a_dim1]), abs(d__2));
}
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
i__3 = i__ + j * a_dim1;
tmp += (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[
i__ + j * a_dim1]), abs(d__2));
}
}
rwork[i__] = tmp;
anorm = max(anorm,tmp);
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tmp = 0.;
if (*capply) {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * a_dim1;
tmp += ((d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[
i__ + j * a_dim1]), abs(d__2))) / c__[j];
}
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
i__3 = j + i__ * a_dim1;
tmp += ((d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[
j + i__ * a_dim1]), abs(d__2))) / c__[j];
}
} else {
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * a_dim1;
tmp += (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[
i__ + j * a_dim1]), abs(d__2));
}
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
i__3 = j + i__ * a_dim1;
tmp += (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[
j + i__ * a_dim1]), abs(d__2));
}
}
rwork[i__] = tmp;
anorm = max(anorm,tmp);
}
}
/* Quick return if possible. */
if (*n == 0) {
ret_val = 1.;
return ret_val;
} else if (anorm == 0.) {
return ret_val;
}
/* Estimate the norm of inv(op(A)). */
ainvnm = 0.;
kase = 0;
L10:
zlacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
if (kase != 0) {
if (kase == 2) {
/* Multiply by R. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
z__1.r = rwork[i__4] * work[i__3].r, z__1.i = rwork[i__4] *
work[i__3].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
}
if (up) {
zpotrs_("U", n, &c__1, &af[af_offset], ldaf, &work[1], n,
info);
} else {
zpotrs_("L", n, &c__1, &af[af_offset], ldaf, &work[1], n,
info);
}
/* Multiply by inv(C). */
if (*capply) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
z__1.r = c__[i__4] * work[i__3].r, z__1.i = c__[i__4] *
work[i__3].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
}
}
} else {
/* Multiply by inv(C'). */
if (*capply) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
z__1.r = c__[i__4] * work[i__3].r, z__1.i = c__[i__4] *
work[i__3].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
}
}
if (up) {
zpotrs_("U", n, &c__1, &af[af_offset], ldaf, &work[1], n,
info);
} else {
zpotrs_("L", n, &c__1, &af[af_offset], ldaf, &work[1], n,
info);
}
/* Multiply by R. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
z__1.r = rwork[i__4] * work[i__3].r, z__1.i = rwork[i__4] *
work[i__3].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
}
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.) {
ret_val = 1. / ainvnm;
}
return ret_val;
} /* zla_porcond_c__ */
/* Subroutine */
int zporfs_(char *uplo, integer *n, integer *nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal * rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
integer i__, j, k;
doublereal s, xk;
integer nz;
doublereal eps;
integer kase;
doublereal safe1, safe2;
extern logical lsame_(char *, char *);
integer isave[3], count;
extern /* Subroutine */
int zhemv_(char *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *);
logical upper;
extern /* Subroutine */
int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *), zlacn2_( integer *, doublecomplex *, doublecomplex *, doublereal *, integer *, integer *);
extern doublereal dlamch_(char *);
doublereal safmin;
extern /* Subroutine */
int xerbla_(char *, integer *);
doublereal lstres;
extern /* Subroutine */
int zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *);
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ==================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
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 (*lda < max(1,*n))
{
*info = -5;
}
else if (*ldaf < max(1,*n))
{
*info = -7;
}
else if (*ldb < max(1,*n))
{
*info = -9;
}
else if (*ldx < max(1,*n))
{
*info = -11;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("ZPORFS", &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.;
berr[j] = 0.;
/* L10: */
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = dlamch_("Epsilon");
safmin = dlamch_("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.;
L20: /* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - A * X */
zcopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
z__1.r = -1.;
z__1.i = -0.; // , expr subst
zhemv_(uplo, n, &z__1, &a[a_offset], lda, &x[j * x_dim1 + 1], &c__1, & c_b1, &work[1], &c__1);
/* Compute componentwise relative backward error from formula */
/* max(i) ( f2c_abs(R(i)) / ( f2c_abs(A)*f2c_abs(X) + f2c_abs(B) )(i) ) */
/* where f2c_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__] = (d__1 = b[i__3].r, f2c_abs(d__1)) + (d__2 = d_imag(&b[ i__ + j * b_dim1]), f2c_abs(d__2));
/* L30: */
}
/* Compute f2c_abs(A)*f2c_abs(X) + f2c_abs(B). */
if (upper)
{
i__2 = *n;
for (k = 1;
k <= i__2;
++k)
{
s = 0.;
i__3 = k + j * x_dim1;
xk = (d__1 = x[i__3].r, f2c_abs(d__1)) + (d__2 = d_imag(&x[k + j * x_dim1]), f2c_abs(d__2));
i__3 = k - 1;
for (i__ = 1;
i__ <= i__3;
++i__)
{
i__4 = i__ + k * a_dim1;
rwork[i__] += ((d__1 = a[i__4].r, f2c_abs(d__1)) + (d__2 = d_imag(&a[i__ + k * a_dim1]), f2c_abs(d__2))) * xk;
i__4 = i__ + k * a_dim1;
i__5 = i__ + j * x_dim1;
s += ((d__1 = a[i__4].r, f2c_abs(d__1)) + (d__2 = d_imag(&a[ i__ + k * a_dim1]), f2c_abs(d__2))) * ((d__3 = x[i__5] .r, f2c_abs(d__3)) + (d__4 = d_imag(&x[i__ + j * x_dim1]), f2c_abs(d__4)));
/* L40: */
}
i__3 = k + k * a_dim1;
rwork[k] = rwork[k] + (d__1 = a[i__3].r, f2c_abs(d__1)) * xk + s;
/* L50: */
}
}
else
{
i__2 = *n;
for (k = 1;
k <= i__2;
++k)
{
s = 0.;
i__3 = k + j * x_dim1;
xk = (d__1 = x[i__3].r, f2c_abs(d__1)) + (d__2 = d_imag(&x[k + j * x_dim1]), f2c_abs(d__2));
i__3 = k + k * a_dim1;
rwork[k] += (d__1 = a[i__3].r, f2c_abs(d__1)) * xk;
i__3 = *n;
for (i__ = k + 1;
i__ <= i__3;
++i__)
{
i__4 = i__ + k * a_dim1;
rwork[i__] += ((d__1 = a[i__4].r, f2c_abs(d__1)) + (d__2 = d_imag(&a[i__ + k * a_dim1]), f2c_abs(d__2))) * xk;
i__4 = i__ + k * a_dim1;
i__5 = i__ + j * x_dim1;
s += ((d__1 = a[i__4].r, f2c_abs(d__1)) + (d__2 = d_imag(&a[ i__ + k * a_dim1]), f2c_abs(d__2))) * ((d__3 = x[i__5] .r, f2c_abs(d__3)) + (d__4 = d_imag(&x[i__ + j * x_dim1]), f2c_abs(d__4)));
/* L60: */
}
rwork[k] += s;
/* L70: */
}
}
s = 0.;
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
if (rwork[i__] > safe2)
{
/* Computing MAX */
i__3 = i__;
d__3 = s;
d__4 = ((d__1 = work[i__3].r, f2c_abs(d__1)) + (d__2 = d_imag(&work[i__]), f2c_abs(d__2))) / rwork[i__]; // , expr subst
s = max(d__3,d__4);
}
else
{
/* Computing MAX */
i__3 = i__;
d__3 = s;
d__4 = ((d__1 = work[i__3].r, f2c_abs(d__1)) + (d__2 = d_imag(&work[i__]), f2c_abs(d__2)) + safe1) / (rwork[i__] + safe1); // , expr subst
s = max(d__3,d__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. <= lstres && count <= 5)
{
/* Update solution and try again. */
zpotrs_(uplo, n, &c__1, &af[af_offset], ldaf, &work[1], n, info);
zaxpy_(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( f2c_abs(inv(A))* */
/* ( f2c_abs(R) + NZ*EPS*( f2c_abs(A)*f2c_abs(X)+f2c_abs(B) ))) / norm(X) */
/* where */
/* norm(Z) is the magnitude of the largest component of Z */
/* inv(A) is the inverse of A */
/* f2c_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 f2c_abs(R)+NZ*EPS*(f2c_abs(A)*f2c_abs(X)+f2c_abs(B)) */
/* is incremented by SAFE1 if the i-th component of */
/* f2c_abs(A)*f2c_abs(X) + f2c_abs(B) is less than SAFE2. */
/* Use ZLACN2 to estimate the infinity-norm of the matrix */
/* inv(A) * diag(W), */
/* where W = f2c_abs(R) + NZ*EPS*( f2c_abs(A)*f2c_abs(X)+f2c_abs(B) ))) */
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
if (rwork[i__] > safe2)
{
i__3 = i__;
rwork[i__] = (d__1 = work[i__3].r, f2c_abs(d__1)) + (d__2 = d_imag(&work[i__]), f2c_abs(d__2)) + nz * eps * rwork[i__] ;
}
else
{
i__3 = i__;
rwork[i__] = (d__1 = work[i__3].r, f2c_abs(d__1)) + (d__2 = d_imag(&work[i__]), f2c_abs(d__2)) + nz * eps * rwork[i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
zlacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
if (kase != 0)
{
if (kase == 1)
{
/* Multiply by diag(W)*inv(A**H). */
zpotrs_(uplo, n, &c__1, &af[af_offset], ldaf, &work[1], n, info);
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__;
i__4 = i__;
i__5 = i__;
z__1.r = rwork[i__4] * work[i__5].r;
z__1.i = rwork[i__4] * work[i__5].i; // , expr subst
work[i__3].r = z__1.r;
work[i__3].i = z__1.i; // , expr subst
/* 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__;
z__1.r = rwork[i__4] * work[i__5].r;
z__1.i = rwork[i__4] * work[i__5].i; // , expr subst
work[i__3].r = z__1.r;
work[i__3].i = z__1.i; // , expr subst
/* L120: */
}
zpotrs_(uplo, n, &c__1, &af[af_offset], ldaf, &work[1], n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.;
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
/* Computing MAX */
i__3 = i__ + j * x_dim1;
d__3 = lstres;
d__4 = (d__1 = x[i__3].r, f2c_abs(d__1)) + (d__2 = d_imag(&x[i__ + j * x_dim1]), f2c_abs(d__2)); // , expr subst
lstres = max(d__3,d__4);
/* L130: */
}
if (lstres != 0.)
{
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of ZPORFS */
}
/* Subroutine */ int zerrpo_(char *path, integer *nunit)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
doublecomplex z__1;
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
static integer info;
static doublereal anrm;
static doublecomplex a[16] /* was [4][4] */, b[4];
static integer i__, j;
static doublereal r__[4];
static doublecomplex w[8], x[4];
static doublereal rcond;
static char c2[2];
static doublereal r1[4], r2[4];
static doublecomplex af[16] /* was [4][4] */;
extern /* Subroutine */ int zpbtf2_(char *, integer *, integer *,
doublecomplex *, integer *, integer *), zpotf2_(char *,
integer *, doublecomplex *, integer *, integer *),
alaesm_(char *, logical *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), zpbcon_(char *, integer *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *), zpbequ_(char *,
integer *, integer *, doublecomplex *, integer *, doublereal *,
doublereal *, doublereal *, integer *), zpbrfs_(char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *), zpbtrf_(char *,
integer *, integer *, doublecomplex *, integer *, integer *), zpocon_(char *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zppcon_(char *, integer *, doublecomplex *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zpoequ_(integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublereal *, integer *), zpbtrs_(
char *, integer *, integer *, integer *, doublecomplex *, integer
*, doublecomplex *, integer *, integer *), zporfs_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *
, integer *, doublecomplex *, integer *, doublecomplex *, integer
*, doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zpotrf_(char *, integer *, doublecomplex *,
integer *, integer *), zpotri_(char *, integer *,
doublecomplex *, integer *, integer *), zppequ_(char *,
integer *, doublecomplex *, doublereal *, doublereal *,
doublereal *, integer *), zpprfs_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *), zpptrf_(char *
, integer *, doublecomplex *, integer *), zpptri_(char *,
integer *, doublecomplex *, integer *), zpotrs_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *), zpptrs_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
#define a_subscr(a_1,a_2) (a_2)*4 + a_1 - 5
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define af_subscr(a_1,a_2) (a_2)*4 + a_1 - 5
#define af_ref(a_1,a_2) af[af_subscr(a_1,a_2)]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
ZERRPO tests the error exits for the COMPLEX*16 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.
===================================================================== */
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 = a_subscr(i__, j);
d__1 = 1. / (doublereal) (i__ + j);
d__2 = -1. / (doublereal) (i__ + j);
z__1.r = d__1, z__1.i = d__2;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = af_subscr(i__, j);
d__1 = 1. / (doublereal) (i__ + j);
d__2 = -1. / (doublereal) (i__ + j);
z__1.r = d__1, z__1.i = d__2;
af[i__1].r = z__1.r, af[i__1].i = z__1.i;
/* L10: */
}
i__1 = j - 1;
b[i__1].r = 0., b[i__1].i = 0.;
r1[j - 1] = 0.;
r2[j - 1] = 0.;
i__1 = j - 1;
w[i__1].r = 0., w[i__1].i = 0.;
i__1 = j - 1;
x[i__1].r = 0., x[i__1].i = 0.;
/* L20: */
}
anrm = 1.;
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")) {
/* ZPOTRF */
s_copy(srnamc_1.srnamt, "ZPOTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpotrf_("/", &c__0, a, &c__1, &info);
chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpotrf_("U", &c_n1, a, &c__1, &info);
chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zpotrf_("U", &c__2, a, &c__1, &info);
chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPOTF2 */
s_copy(srnamc_1.srnamt, "ZPOTF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpotf2_("/", &c__0, a, &c__1, &info);
chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpotf2_("U", &c_n1, a, &c__1, &info);
chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zpotf2_("U", &c__2, a, &c__1, &info);
chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPOTRI */
s_copy(srnamc_1.srnamt, "ZPOTRI", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpotri_("/", &c__0, a, &c__1, &info);
chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpotri_("U", &c_n1, a, &c__1, &info);
chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zpotri_("U", &c__2, a, &c__1, &info);
chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPOTRS */
s_copy(srnamc_1.srnamt, "ZPOTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpotrs_("/", &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpotrs_("U", &c_n1, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpotrs_("U", &c__0, &c_n1, a, &c__1, b, &c__1, &info);
chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zpotrs_("U", &c__2, &c__1, a, &c__1, b, &c__2, &info);
chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zpotrs_("U", &c__2, &c__1, a, &c__2, b, &c__1, &info);
chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPORFS */
s_copy(srnamc_1.srnamt, "ZPORFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zporfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zporfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zporfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zporfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &c__2,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &c__2,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__1, x, &c__2,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__2, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPOCON */
s_copy(srnamc_1.srnamt, "ZPOCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpocon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpocon_("U", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zpocon_("U", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
d__1 = -anrm;
zpocon_("U", &c__1, a, &c__1, &d__1, &rcond, w, r__, &info)
;
chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPOEQU */
s_copy(srnamc_1.srnamt, "ZPOEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpoequ_(&c_n1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpoequ_(&c__2, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("ZPOEQU", &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")) {
/* ZPPTRF */
s_copy(srnamc_1.srnamt, "ZPPTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpptrf_("/", &c__0, a, &info);
chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpptrf_("U", &c_n1, a, &info);
chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPPTRI */
s_copy(srnamc_1.srnamt, "ZPPTRI", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpptri_("/", &c__0, a, &info);
chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpptri_("U", &c_n1, a, &info);
chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPPTRS */
s_copy(srnamc_1.srnamt, "ZPPTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpptrs_("/", &c__0, &c__0, a, b, &c__1, &info);
chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpptrs_("U", &c_n1, &c__0, a, b, &c__1, &info);
chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpptrs_("U", &c__0, &c_n1, a, b, &c__1, &info);
chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zpptrs_("U", &c__2, &c__1, a, b, &c__1, &info);
chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPPRFS */
s_copy(srnamc_1.srnamt, "ZPPRFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpprfs_("/", &c__0, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpprfs_("U", &c_n1, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpprfs_("U", &c__0, &c_n1, a, af, b, &c__1, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zpprfs_("U", &c__2, &c__1, a, af, b, &c__1, x, &c__2, r1, r2, w, r__,
&info);
chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
zpprfs_("U", &c__2, &c__1, a, af, b, &c__2, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPPCON */
s_copy(srnamc_1.srnamt, "ZPPCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zppcon_("/", &c__0, a, &anrm, &rcond, w, r__, &info);
chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zppcon_("U", &c_n1, a, &anrm, &rcond, w, r__, &info);
chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
d__1 = -anrm;
zppcon_("U", &c__1, a, &d__1, &rcond, w, r__, &info);
chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPPEQU */
s_copy(srnamc_1.srnamt, "ZPPEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zppequ_("/", &c__0, a, r1, &rcond, &anrm, &info);
chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zppequ_("U", &c_n1, a, r1, &rcond, &anrm, &info);
chkxer_("ZPPEQU", &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")) {
/* ZPBTRF */
s_copy(srnamc_1.srnamt, "ZPBTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpbtrf_("/", &c__0, &c__0, a, &c__1, &info);
chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpbtrf_("U", &c_n1, &c__0, a, &c__1, &info);
chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpbtrf_("U", &c__1, &c_n1, a, &c__1, &info);
chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zpbtrf_("U", &c__2, &c__1, a, &c__1, &info);
chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPBTF2 */
s_copy(srnamc_1.srnamt, "ZPBTF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpbtf2_("/", &c__0, &c__0, a, &c__1, &info);
chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpbtf2_("U", &c_n1, &c__0, a, &c__1, &info);
chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpbtf2_("U", &c__1, &c_n1, a, &c__1, &info);
chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zpbtf2_("U", &c__2, &c__1, a, &c__1, &info);
chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPBTRS */
s_copy(srnamc_1.srnamt, "ZPBTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpbtrs_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpbtrs_("U", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpbtrs_("U", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zpbtrs_("U", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, &info);
chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zpbtrs_("U", &c__2, &c__1, &c__1, a, &c__1, b, &c__1, &info);
chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zpbtrs_("U", &c__2, &c__0, &c__1, a, &c__1, b, &c__1, &info);
chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPBRFS */
s_copy(srnamc_1.srnamt, "ZPBRFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpbrfs_("/", &c__0, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
zpbrfs_("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_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPBCON */
s_copy(srnamc_1.srnamt, "ZPBCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpbcon_("/", &c__0, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpbcon_("U", &c_n1, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpbcon_("U", &c__1, &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zpbcon_("U", &c__2, &c__1, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
d__1 = -anrm;
zpbcon_("U", &c__1, &c__0, a, &c__1, &d__1, &rcond, w, r__, &info);
chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZPBEQU */
s_copy(srnamc_1.srnamt, "ZPBEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zpbequ_("/", &c__0, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zpbequ_("U", &c_n1, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zpbequ_("U", &c__1, &c_n1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zpbequ_("U", &c__2, &c__1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("ZPBEQU", &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 ZERRPO */
} /* zerrpo_ */
/* Subroutine */ int ztimpo_(char *line, integer *nn, integer *nval, integer *
nns, integer *nsval, integer *nnb, integer *nbval, integer *nlda,
integer *ldaval, doublereal *timmin, doublecomplex *a, doublecomplex *
b, integer *iwork, doublereal *reslts, integer *ldr1, integer *ldr2,
integer *ldr3, integer *nout, ftnlen line_len)
{
/* Initialized data */
static char uplos[1*2] = "U" "L";
static char subnam[6*3] = "ZPOTRF" "ZPOTRS" "ZPOTRI";
/* Format strings */
static char fmt_9999[] = "(1x,a6,\002 timing run not attempted\002,/)";
static char fmt_9998[] = "(/\002 *** Speed of \002,a6,\002 in megaflops "
"***\002)";
static char fmt_9997[] = "(5x,\002line \002,i2,\002 with LDA = \002,i5)";
static char fmt_9996[] = "(5x,a6,\002 with UPLO = '\002,a1,\002'\002,/)";
/* System generated locals */
integer reslts_dim1, reslts_dim2, reslts_dim3, reslts_offset, i__1, i__2,
i__3;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void),
s_wsle(cilist *), e_wsle(void);
/* Local variables */
static integer ilda, info;
static char path[3];
static doublereal time;
static integer isub, nrhs;
static char uplo[1];
static integer i__, n;
static char cname[6];
extern doublereal dopla_(char *, integer *, integer *, integer *, integer
*, integer *);
extern logical lsame_(char *, char *);
static integer iuplo, i3;
static doublereal s1, s2;
static integer ic, nb, in;
extern doublereal dsecnd_(void);
extern /* Subroutine */ int atimck_(integer *, char *, integer *, integer
*, integer *, integer *, integer *, integer *, ftnlen);
extern doublereal dmflop_(doublereal *, doublereal *, integer *);
extern /* Subroutine */ int atimin_(char *, char *, integer *, char *,
logical *, integer *, integer *, ftnlen, ftnlen, ftnlen), dprtbl_(
char *, char *, integer *, integer *, integer *, integer *,
integer *, doublereal *, integer *, integer *, integer *, ftnlen,
ftnlen), xlaenv_(integer *, integer *);
static doublereal untime;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
static logical timsub[3];
extern /* Subroutine */ int ztimmg_(integer *, integer *, integer *,
doublecomplex *, integer *, integer *, integer *), zpotrf_(char *,
integer *, doublecomplex *, integer *, integer *),
zpotri_(char *, integer *, doublecomplex *, integer *, integer *), zpotrs_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, integer *);
static integer lda, ldb, icl, inb, mat;
static doublereal ops;
/* Fortran I/O blocks */
static cilist io___7 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___29 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___30 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___31 = { 0, 0, 0, 0, 0 };
static cilist io___32 = { 0, 0, 0, fmt_9996, 0 };
#define subnam_ref(a_0,a_1) &subnam[(a_1)*6 + a_0 - 6]
#define reslts_ref(a_1,a_2,a_3,a_4) reslts[(((a_4)*reslts_dim3 + (a_3))*\
reslts_dim2 + (a_2))*reslts_dim1 + a_1]
/* -- LAPACK timing 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
=======
ZTIMPO times ZPOTRF, -TRS, and -TRI.
Arguments
=========
LINE (input) CHARACTER*80
The input line that requested this routine. The first six
characters contain either the name of a subroutine or a
generic path name. The remaining characters may be used to
specify the individual routines to be timed. See ATIMIN for
a full description of the format of the input line.
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 size N.
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.
NNB (input) INTEGER
The number of values of NB contained in the vector NBVAL.
NBVAL (input) INTEGER array, dimension (NNB)
The values of the blocksize NB.
NLDA (input) INTEGER
The number of values of LDA contained in the vector LDAVAL.
LDAVAL (input) INTEGER array, dimension (NLDA)
The values of the leading dimension of the array A.
TIMMIN (input) DOUBLE PRECISION
The minimum time a subroutine will be timed.
A (workspace) COMPLEX*16 array, dimension (LDAMAX*NMAX)
where LDAMAX and NMAX are the maximum values permitted
for LDA and N.
B (workspace) COMPLEX*16 array, dimension (LDAMAX*NMAX)
IWORK (workspace) INTEGER array, dimension (NMAX)
RESLTS (output) DOUBLE PRECISION array, dimension
(LDR1,LDR2,LDR3,NSUBS)
The timing results for each subroutine over the relevant
values of N, NB, and LDA.
LDR1 (input) INTEGER
The first dimension of RESLTS. LDR1 >= max(4,NNB).
LDR2 (input) INTEGER
The second dimension of RESLTS. LDR2 >= max(1,NN).
LDR3 (input) INTEGER
The third dimension of RESLTS. LDR3 >= max(1,2*NLDA).
NOUT (input) INTEGER
The unit number for output.
=====================================================================
Parameter adjustments */
--nval;
--nsval;
--nbval;
--ldaval;
--a;
--b;
--iwork;
reslts_dim1 = *ldr1;
reslts_dim2 = *ldr2;
reslts_dim3 = *ldr3;
reslts_offset = 1 + reslts_dim1 * (1 + reslts_dim2 * (1 + reslts_dim3 * 1)
);
reslts -= reslts_offset;
/* Function Body
Extract the timing request from the input line. */
s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "PO", (ftnlen)2, (ftnlen)2);
atimin_(path, line, &c__3, subnam, timsub, nout, &info, (ftnlen)3, (
ftnlen)80, (ftnlen)6);
if (info != 0) {
goto L150;
}
/* Check that N <= LDA for the input values. */
s_copy(cname, line, (ftnlen)6, (ftnlen)6);
atimck_(&c__2, cname, nn, &nval[1], nlda, &ldaval[1], nout, &info, (
ftnlen)6);
if (info > 0) {
io___7.ciunit = *nout;
s_wsfe(&io___7);
do_fio(&c__1, cname, (ftnlen)6);
e_wsfe();
goto L150;
}
/* Do first for UPLO = 'U', then for UPLO = 'L' */
for (iuplo = 1; iuplo <= 2; ++iuplo) {
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
if (lsame_(uplo, "U")) {
mat = 3;
} else {
mat = -3;
}
/* Do for each value of N in NVAL. */
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
n = nval[in];
/* Do for each value of LDA: */
i__2 = *nlda;
for (ilda = 1; ilda <= i__2; ++ilda) {
lda = ldaval[ilda];
i3 = (iuplo - 1) * *nlda + ilda;
/* Do for each value of NB in NBVAL. Only the blocked
routines are timed in this loop since the other routines
are independent of NB. */
i__3 = *nnb;
for (inb = 1; inb <= i__3; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
/* Time ZPOTRF */
if (timsub[0]) {
ztimmg_(&mat, &n, &n, &a[1], &lda, &c__0, &c__0);
ic = 0;
s1 = dsecnd_();
L10:
zpotrf_(uplo, &n, &a[1], &lda, &info);
s2 = dsecnd_();
time = s2 - s1;
++ic;
if (time < *timmin) {
ztimmg_(&mat, &n, &n, &a[1], &lda, &c__0, &c__0);
goto L10;
}
/* Subtract the time used in ZTIMMG. */
icl = 1;
s1 = dsecnd_();
L20:
s2 = dsecnd_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
ztimmg_(&mat, &n, &n, &a[1], &lda, &c__0, &c__0);
goto L20;
}
time = (time - untime) / (doublereal) ic;
ops = dopla_("ZPOTRF", &n, &n, &c__0, &c__0, &nb);
reslts_ref(inb, in, i3, 1) = dmflop_(&ops, &time, &
info);
} else {
ic = 0;
ztimmg_(&mat, &n, &n, &a[1], &lda, &c__0, &c__0);
}
/* Generate another matrix and factor it using ZPOTRF so
that the factored form can be used in timing the other
routines. */
if (ic != 1) {
zpotrf_(uplo, &n, &a[1], &lda, &info);
}
/* Time ZPOTRI */
if (timsub[2]) {
zlacpy_(uplo, &n, &n, &a[1], &lda, &b[1], &lda);
ic = 0;
s1 = dsecnd_();
L30:
zpotri_(uplo, &n, &b[1], &lda, &info);
s2 = dsecnd_();
time = s2 - s1;
++ic;
if (time < *timmin) {
zlacpy_(uplo, &n, &n, &a[1], &lda, &b[1], &lda);
goto L30;
}
/* Subtract the time used in ZLACPY. */
icl = 1;
s1 = dsecnd_();
L40:
s2 = dsecnd_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
zlacpy_(uplo, &n, &n, &a[1], &lda, &b[1], &lda);
goto L40;
}
time = (time - untime) / (doublereal) ic;
ops = dopla_("ZPOTRI", &n, &n, &c__0, &c__0, &nb);
reslts_ref(inb, in, i3, 3) = dmflop_(&ops, &time, &
info);
}
/* L50: */
}
/* Time ZPOTRS */
if (timsub[1]) {
i__3 = *nns;
for (i__ = 1; i__ <= i__3; ++i__) {
nrhs = nsval[i__];
ldb = lda;
ztimmg_(&c__0, &n, &nrhs, &b[1], &ldb, &c__0, &c__0);
ic = 0;
s1 = dsecnd_();
L60:
zpotrs_(uplo, &n, &nrhs, &a[1], &lda, &b[1], &ldb, &
info);
s2 = dsecnd_();
time = s2 - s1;
++ic;
if (time < *timmin) {
ztimmg_(&c__0, &n, &nrhs, &b[1], &ldb, &c__0, &
c__0);
goto L60;
}
/* Subtract the time used in ZTIMMG. */
icl = 1;
s1 = dsecnd_();
L70:
s2 = dsecnd_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
ztimmg_(&c__0, &n, &nrhs, &b[1], &ldb, &c__0, &
c__0);
goto L70;
}
time = (time - untime) / (doublereal) ic;
ops = dopla_("ZPOTRS", &n, &nrhs, &c__0, &c__0, &c__0);
reslts_ref(i__, in, i3, 2) = dmflop_(&ops, &time, &
info);
/* L80: */
}
}
/* L90: */
}
/* L100: */
}
/* L110: */
}
/* Print tables of results for each timed routine. */
for (isub = 1; isub <= 3; ++isub) {
if (! timsub[isub - 1]) {
goto L140;
}
io___29.ciunit = *nout;
s_wsfe(&io___29);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
if (*nlda > 1) {
i__1 = *nlda;
for (i__ = 1; i__ <= i__1; ++i__) {
io___30.ciunit = *nout;
s_wsfe(&io___30);
do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ldaval[i__], (ftnlen)sizeof(integer));
e_wsfe();
/* L120: */
}
}
io___31.ciunit = *nout;
s_wsle(&io___31);
e_wsle();
for (iuplo = 1; iuplo <= 2; ++iuplo) {
io___32.ciunit = *nout;
s_wsfe(&io___32);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
do_fio(&c__1, uplos + (iuplo - 1), (ftnlen)1);
e_wsfe();
i3 = (iuplo - 1) * *nlda + 1;
if (isub == 1) {
dprtbl_("NB", "N", nnb, &nbval[1], nn, &nval[1], nlda, &
reslts_ref(1, 1, i3, 1), ldr1, ldr2, nout, (ftnlen)2,
(ftnlen)1);
} else if (isub == 2) {
dprtbl_("NRHS", "N", nns, &nsval[1], nn, &nval[1], nlda, &
reslts_ref(1, 1, i3, 2), ldr1, ldr2, nout, (ftnlen)4,
(ftnlen)1);
} else if (isub == 3) {
dprtbl_("NB", "N", nnb, &nbval[1], nn, &nval[1], nlda, &
reslts_ref(1, 1, i3, 3), ldr1, ldr2, nout, (ftnlen)2,
(ftnlen)1);
}
/* L130: */
}
L140:
;
}
L150:
return 0;
/* End of ZTIMPO */
} /* ztimpo_ */
/* Subroutine */ int zchkpo_(logical *dotype, integer *nn, integer *nval,
integer *nnb, integer *nbval, integer *nns, integer *nsval,
doublereal *thresh, logical *tsterr, integer *nmax, doublecomplex *a,
doublecomplex *afac, doublecomplex *ainv, doublecomplex *b,
doublecomplex *x, doublecomplex *xact, doublecomplex *work,
doublereal *rwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char uplos[1*2] = "U" "L";
/* Format strings */
static char fmt_9999[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, "
"NB =\002,i4,\002, type \002,i2,\002, test \002,i2,\002, ratio "
"=\002,g12.5)";
static char fmt_9998[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, "
"NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g"
"12.5)";
static char fmt_9997[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002"
",\002,10x,\002 type \002,i2,\002, test(\002,i2,\002) =\002,g12.5)"
;
/* System generated locals */
integer i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, k, n, nb, in, kl, ku, lda, inb, ioff, mode, imat, info;
char path[3], dist[1];
integer irhs, nrhs;
char uplo[1], type__[1];
integer nrun;
integer nfail, iseed[4];
doublereal rcond;
integer nimat;
doublereal anorm;
integer iuplo, izero, nerrs;
logical zerot;
char xtype[1];
doublereal rcondc;
doublereal cndnum;
doublereal result[8];
/* Fortran I/O blocks */
static cilist io___33 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___36 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___38 = { 0, 0, 0, fmt_9997, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZCHKPO tests ZPOTRF, -TRI, -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. */
/* 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. */
/* 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. */
/* NMAX (input) INTEGER */
/* The maximum value permitted for N, used in dimensioning the */
/* work arrays. */
/* A (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* AFAC (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* AINV (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* B (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* where NSMAX is the largest entry in NSVAL. */
/* 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)) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension */
/* (NMAX+2*NSMAX) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--rwork;
--work;
--xact;
--x;
--b;
--ainv;
--afac;
--a;
--nsval;
--nbval;
--nval;
--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, "PO", (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) {
zerrpo_(path, nout);
}
infoc_1.infot = 0;
/* Do for each value of N in NVAL */
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
n = nval[in];
lda = max(n,1);
*(unsigned char *)xtype = 'N';
nimat = 9;
if (n <= 0) {
nimat = 1;
}
izero = 0;
i__2 = nimat;
for (imat = 1; imat <= i__2; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L110;
}
/* Skip types 3, 4, or 5 if the matrix size is too small. */
zerot = imat >= 3 && imat <= 5;
if (zerot && n < imat - 2) {
goto L110;
}
/* Do first for UPLO = 'U', then for UPLO = 'L' */
for (iuplo = 1; iuplo <= 2; ++iuplo) {
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
/* Set up parameters with ZLATB4 and generate a test matrix */
/* with ZLATMS. */
zlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode,
&cndnum, dist);
s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)32, (ftnlen)6);
zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &
cndnum, &anorm, &kl, &ku, uplo, &a[1], &lda, &work[1],
&info);
/* Check error code from ZLATMS. */
if (info != 0) {
alaerh_(path, "ZLATMS", &info, &c__0, uplo, &n, &n, &c_n1,
&c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
goto L100;
}
/* For types 3-5, zero one row and column of the matrix to */
/* test that INFO is returned correctly. */
if (zerot) {
if (imat == 3) {
izero = 1;
} else if (imat == 4) {
izero = n;
} else {
izero = n / 2 + 1;
}
ioff = (izero - 1) * lda;
/* Set row and column IZERO of A to 0. */
if (iuplo == 1) {
i__3 = izero - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = ioff + i__;
a[i__4].r = 0., a[i__4].i = 0.;
/* L20: */
}
ioff += izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
i__4 = ioff;
a[i__4].r = 0., a[i__4].i = 0.;
ioff += lda;
/* L30: */
}
} else {
ioff = izero;
i__3 = izero - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = ioff;
a[i__4].r = 0., a[i__4].i = 0.;
ioff += lda;
/* L40: */
}
ioff -= izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
i__4 = ioff + i__;
a[i__4].r = 0., a[i__4].i = 0.;
/* L50: */
}
}
} else {
izero = 0;
}
/* Set the imaginary part of the diagonals. */
i__3 = lda + 1;
zlaipd_(&n, &a[1], &i__3, &c__0);
/* Do for each value of NB in NBVAL */
i__3 = *nnb;
for (inb = 1; inb <= i__3; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
/* Compute the L*L' or U'*U factorization of the matrix. */
zlacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda);
s_copy(srnamc_1.srnamt, "ZPOTRF", (ftnlen)32, (ftnlen)6);
zpotrf_(uplo, &n, &afac[1], &lda, &info);
/* Check error code from ZPOTRF. */
if (info != izero) {
alaerh_(path, "ZPOTRF", &info, &izero, uplo, &n, &n, &
c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout);
goto L90;
}
/* Skip the tests if INFO is not 0. */
if (info != 0) {
goto L90;
}
/* + TEST 1 */
/* Reconstruct matrix from factors and compute residual. */
zlacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda);
zpot01_(uplo, &n, &a[1], &lda, &ainv[1], &lda, &rwork[1],
result);
/* + TEST 2 */
/* Form the inverse and compute the residual. */
zlacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda);
s_copy(srnamc_1.srnamt, "ZPOTRI", (ftnlen)32, (ftnlen)6);
zpotri_(uplo, &n, &ainv[1], &lda, &info);
/* Check error code from ZPOTRI. */
if (info != 0) {
alaerh_(path, "ZPOTRI", &info, &c__0, uplo, &n, &n, &
c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs,
nout);
}
zpot03_(uplo, &n, &a[1], &lda, &ainv[1], &lda, &work[1], &
lda, &rwork[1], &rcondc, &result[1]);
/* Print information about the tests that did not pass */
/* the threshold. */
for (k = 1; k <= 2; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___33.ciunit = *nout;
s_wsfe(&io___33);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (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 *)&k, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
sizeof(doublereal));
e_wsfe();
++nfail;
}
/* L60: */
}
nrun += 2;
/* Skip the rest of the tests unless this is the first */
/* blocksize. */
if (inb != 1) {
goto L90;
}
i__4 = *nns;
for (irhs = 1; irhs <= i__4; ++irhs) {
nrhs = nsval[irhs];
/* + TEST 3 */
/* Solve and compute residual for A * X = B . */
s_copy(srnamc_1.srnamt, "ZLARHS", (ftnlen)32, (ftnlen)
6);
zlarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, &
nrhs, &a[1], &lda, &xact[1], &lda, &b[1], &
lda, iseed, &info);
zlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda);
s_copy(srnamc_1.srnamt, "ZPOTRS", (ftnlen)32, (ftnlen)
6);
zpotrs_(uplo, &n, &nrhs, &afac[1], &lda, &x[1], &lda,
&info);
/* Check error code from ZPOTRS. */
if (info != 0) {
alaerh_(path, "ZPOTRS", &info, &c__0, uplo, &n, &
n, &c_n1, &c_n1, &nrhs, &imat, &nfail, &
nerrs, nout);
}
zlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &
lda);
zpot02_(uplo, &n, &nrhs, &a[1], &lda, &x[1], &lda, &
work[1], &lda, &rwork[1], &result[2]);
/* + TEST 4 */
/* Check solution from generated exact solution. */
zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[3]);
/* + TESTS 5, 6, and 7 */
/* Use iterative refinement to improve the solution. */
s_copy(srnamc_1.srnamt, "ZPORFS", (ftnlen)32, (ftnlen)
6);
zporfs_(uplo, &n, &nrhs, &a[1], &lda, &afac[1], &lda,
&b[1], &lda, &x[1], &lda, &rwork[1], &rwork[
nrhs + 1], &work[1], &rwork[(nrhs << 1) + 1],
&info);
/* Check error code from ZPORFS. */
if (info != 0) {
alaerh_(path, "ZPORFS", &info, &c__0, uplo, &n, &
n, &c_n1, &c_n1, &nrhs, &imat, &nfail, &
nerrs, nout);
}
zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[4]);
zpot05_(uplo, &n, &nrhs, &a[1], &lda, &b[1], &lda, &x[
1], &lda, &xact[1], &lda, &rwork[1], &rwork[
nrhs + 1], &result[5]);
/* Print information about the tests that did not pass */
/* the threshold. */
for (k = 3; k <= 7; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___36.ciunit = *nout;
s_wsfe(&io___36);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (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;
}
/* L70: */
}
nrun += 5;
/* L80: */
}
/* + TEST 8 */
/* Get an estimate of RCOND = 1/CNDNUM. */
anorm = zlanhe_("1", uplo, &n, &a[1], &lda, &rwork[1]);
s_copy(srnamc_1.srnamt, "ZPOCON", (ftnlen)32, (ftnlen)6);
zpocon_(uplo, &n, &afac[1], &lda, &anorm, &rcond, &work[1]
, &rwork[1], &info);
/* Check error code from ZPOCON. */
if (info != 0) {
alaerh_(path, "ZPOCON", &info, &c__0, uplo, &n, &n, &
c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs,
nout);
}
result[7] = dget06_(&rcond, &rcondc);
/* Print the test ratio if it is .GE. THRESH. */
if (result[7] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___38.ciunit = *nout;
s_wsfe(&io___38);
do_fio(&c__1, uplo, (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 *)&c__8, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
++nrun;
L90:
;
}
L100:
;
}
L110:
;
}
/* L120: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of ZCHKPO */
} /* zchkpo_ */
/* Subroutine */ int zporfs_(char *uplo, integer *n, integer *nrhs,
doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf,
doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx,
doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal *
rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1;
/* Local variables */
integer i__, j, k;
doublereal s, xk;
integer nz;
doublereal eps;
integer kase;
doublereal safe1, safe2;
integer isave[3], count;
logical upper;
doublereal safmin;
doublereal lstres;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. */
/* Purpose */
/* ======= */
/* ZPORFS improves the computed solution to a system of linear */
/* equations when the coefficient matrix is Hermitian positive definite, */
/* 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. */
/* A (input) COMPLEX*16 array, dimension (LDA,N) */
/* The Hermitian matrix A. If UPLO = 'U', the leading N-by-N */
/* upper triangular part of A contains the upper triangular part */
/* of the matrix A, and the strictly lower triangular part of A */
/* is not referenced. If UPLO = 'L', the leading N-by-N lower */
/* triangular part of A contains the lower triangular part of */
/* the matrix A, and the strictly upper triangular part of A is */
/* not referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input) COMPLEX*16 array, dimension (LDAF,N) */
/* The triangular factor U or L from the Cholesky factorization */
/* A = U**H*U or A = L*L**H, as computed by ZPOTRF. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* B (input) COMPLEX*16 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*16 array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by ZPOTRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* FERR (output) DOUBLE PRECISION 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) 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 (2*N) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Internal Parameters */
/* =================== */
/* ITMAX is the maximum number of steps of iterative refinement. */
/* ==================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
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 (*lda < max(1,*n)) {
*info = -5;
} else if (*ldaf < max(1,*n)) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -9;
} else if (*ldx < max(1,*n)) {
*info = -11;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPORFS", &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.;
berr[j] = 0.;
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = dlamch_("Epsilon");
safmin = dlamch_("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.;
L20:
/* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - A * X */
zcopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
z__1.r = -1., z__1.i = -0.;
zhemv_(uplo, n, &z__1, &a[a_offset], lda, &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__] = (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(&b[
i__ + j * b_dim1]), abs(d__2));
}
/* Compute abs(A)*abs(X) + abs(B). */
if (upper) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.;
i__3 = k + j * x_dim1;
xk = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[k + j *
x_dim1]), abs(d__2));
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + k * a_dim1;
rwork[i__] += ((d__1 = a[i__4].r, abs(d__1)) + (d__2 =
d_imag(&a[i__ + k * a_dim1]), abs(d__2))) * xk;
i__4 = i__ + k * a_dim1;
i__5 = i__ + j * x_dim1;
s += ((d__1 = a[i__4].r, abs(d__1)) + (d__2 = d_imag(&a[
i__ + k * a_dim1]), abs(d__2))) * ((d__3 = x[i__5]
.r, abs(d__3)) + (d__4 = d_imag(&x[i__ + j *
x_dim1]), abs(d__4)));
}
i__3 = k + k * a_dim1;
rwork[k] = rwork[k] + (d__1 = a[i__3].r, abs(d__1)) * xk + s;
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.;
i__3 = k + j * x_dim1;
xk = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[k + j *
x_dim1]), abs(d__2));
i__3 = k + k * a_dim1;
rwork[k] += (d__1 = a[i__3].r, abs(d__1)) * xk;
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = i__ + k * a_dim1;
rwork[i__] += ((d__1 = a[i__4].r, abs(d__1)) + (d__2 =
d_imag(&a[i__ + k * a_dim1]), abs(d__2))) * xk;
i__4 = i__ + k * a_dim1;
i__5 = i__ + j * x_dim1;
s += ((d__1 = a[i__4].r, abs(d__1)) + (d__2 = d_imag(&a[
i__ + k * a_dim1]), abs(d__2))) * ((d__3 = x[i__5]
.r, abs(d__3)) + (d__4 = d_imag(&x[i__ + j *
x_dim1]), abs(d__4)));
}
rwork[k] += s;
}
}
s = 0.;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__3 = i__;
d__3 = s, d__4 = ((d__1 = work[i__3].r, abs(d__1)) + (d__2 =
d_imag(&work[i__]), abs(d__2))) / rwork[i__];
s = max(d__3,d__4);
} else {
/* Computing MAX */
i__3 = i__;
d__3 = s, d__4 = ((d__1 = work[i__3].r, abs(d__1)) + (d__2 =
d_imag(&work[i__]), abs(d__2)) + safe1) / (rwork[i__]
+ safe1);
s = max(d__3,d__4);
}
}
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. <= lstres && count <= 5) {
/* Update solution and try again. */
zpotrs_(uplo, n, &c__1, &af[af_offset], ldaf, &work[1], n, info);
zaxpy_(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 ZLACN2 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__] = (d__1 = work[i__3].r, abs(d__1)) + (d__2 =
d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
;
} else {
i__3 = i__;
rwork[i__] = (d__1 = work[i__3].r, abs(d__1)) + (d__2 =
d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
+ safe1;
}
}
kase = 0;
L100:
zlacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(A'). */
zpotrs_(uplo, n, &c__1, &af[af_offset], ldaf, &work[1], n,
info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
z__1.r = rwork[i__4] * work[i__5].r, z__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
}
} 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__;
z__1.r = rwork[i__4] * work[i__5].r, z__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
}
zpotrs_(uplo, n, &c__1, &af[af_offset], ldaf, &work[1], n,
info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * x_dim1;
d__3 = lstres, d__4 = (d__1 = x[i__3].r, abs(d__1)) + (d__2 =
d_imag(&x[i__ + j * x_dim1]), abs(d__2));
lstres = max(d__3,d__4);
}
if (lstres != 0.) {
ferr[j] /= lstres;
}
}
return 0;
/* End of ZPORFS */
} /* zporfs_ */
/* Subroutine */
int zla_porfsx_extended_(integer *prec_type__, char *uplo, integer *n, integer *nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf, logical *colequ, doublereal *c__, doublecomplex *b, integer *ldb, doublecomplex *y, integer *ldy, doublereal *berr_out__, integer *n_norms__, doublereal * err_bnds_norm__, doublereal *err_bnds_comp__, doublecomplex *res, doublereal *ayb, doublecomplex *dy, doublecomplex *y_tail__, doublereal *rcond, integer *ithresh, doublereal *rthresh, doublereal * dz_ub__, logical *ignore_cwise__, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, y_dim1, y_offset, err_bnds_norm_dim1, err_bnds_norm_offset, err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
doublereal dxratmax, dzratmax;
integer i__, j;
logical incr_prec__;
extern /* Subroutine */
int zla_heamv_(integer *, integer *, doublereal * , doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, integer *);
doublereal prev_dz_z__, yk, final_dx_x__, final_dz_z__;
extern /* Subroutine */
int zla_wwaddw_(integer *, doublecomplex *, doublecomplex *, doublecomplex *);
doublereal prevnormdx;
integer cnt;
doublereal dyk, eps, incr_thresh__, dx_x__, dz_z__, ymin;
extern /* Subroutine */
int zla_lin_berr_(integer *, integer *, integer * , doublecomplex *, doublereal *, doublereal *);
integer y_prec_state__;
extern /* Subroutine */
int blas_zhemv_x_(integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *) ;
integer uplo2;
extern logical lsame_(char *, char *);
extern /* Subroutine */
int blas_zhemv2_x_(integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *);
doublereal dxrat, dzrat;
extern /* Subroutine */
int zhemv_(char *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *);
doublereal normx, normy;
extern /* Subroutine */
int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *);
extern doublereal dlamch_(char *);
doublereal normdx;
extern /* Subroutine */
int zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *);
doublereal hugeval;
extern integer ilauplo_(char *);
integer x_state__, z_state__;
/* -- LAPACK computational routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Parameters .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. Executable Statements .. */
/* 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;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1;
y -= y_offset;
--berr_out__;
--res;
--ayb;
--dy;
--y_tail__;
/* Function Body */
if (*info != 0)
{
return 0;
}
eps = dlamch_("Epsilon");
hugeval = dlamch_("Overflow");
/* Force HUGEVAL to Inf */
hugeval *= hugeval;
/* Using HUGEVAL may lead to spurious underflows. */
incr_thresh__ = (doublereal) (*n) * eps;
if (lsame_(uplo, "L"))
{
uplo2 = ilauplo_("L");
}
else
{
uplo2 = ilauplo_("U");
}
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
y_prec_state__ = 1;
if (y_prec_state__ == 2)
{
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__;
y_tail__[i__3].r = 0.;
y_tail__[i__3].i = 0.; // , expr subst
}
}
dxrat = 0.;
dxratmax = 0.;
dzrat = 0.;
dzratmax = 0.;
final_dx_x__ = hugeval;
final_dz_z__ = hugeval;
prevnormdx = hugeval;
prev_dz_z__ = hugeval;
dz_z__ = hugeval;
dx_x__ = hugeval;
x_state__ = 1;
z_state__ = 0;
incr_prec__ = FALSE_;
i__2 = *ithresh;
for (cnt = 1;
cnt <= i__2;
++cnt)
{
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
zcopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
if (y_prec_state__ == 0)
{
zhemv_(uplo, n, &c_b11, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, &c_b12, &res[1], &c__1);
}
else if (y_prec_state__ == 1)
{
blas_zhemv_x_(&uplo2, n, &c_b11, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, &c_b12, &res[1], &c__1, prec_type__);
}
else
{
blas_zhemv2_x_(&uplo2, n, &c_b11, &a[a_offset], lda, &y[j * y_dim1 + 1], &y_tail__[1], &c__1, &c_b12, &res[1], & c__1, prec_type__);
}
/* XXX: RES is no longer needed. */
zcopy_(n, &res[1], &c__1, &dy[1], &c__1);
zpotrs_(uplo, n, &c__1, &af[af_offset], ldaf, &dy[1], n, info);
/* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */
normx = 0.;
normy = 0.;
normdx = 0.;
dz_z__ = 0.;
ymin = hugeval;
i__3 = *n;
for (i__ = 1;
i__ <= i__3;
++i__)
{
i__4 = i__ + j * y_dim1;
yk = (d__1 = y[i__4].r, abs(d__1)) + (d__2 = d_imag(&y[i__ + j * y_dim1]), abs(d__2));
i__4 = i__;
dyk = (d__1 = dy[i__4].r, abs(d__1)) + (d__2 = d_imag(&dy[i__] ), abs(d__2));
if (yk != 0.)
{
/* Computing MAX */
d__1 = dz_z__;
d__2 = dyk / yk; // , expr subst
dz_z__ = max(d__1,d__2);
}
else if (dyk != 0.)
{
dz_z__ = hugeval;
}
ymin = min(ymin,yk);
normy = max(normy,yk);
if (*colequ)
{
/* Computing MAX */
d__1 = normx;
d__2 = yk * c__[i__]; // , expr subst
normx = max(d__1,d__2);
/* Computing MAX */
d__1 = normdx;
d__2 = dyk * c__[i__]; // , expr subst
normdx = max(d__1,d__2);
}
else
{
normx = normy;
normdx = max(normdx,dyk);
}
}
if (normx != 0.)
{
dx_x__ = normdx / normx;
}
else if (normdx == 0.)
{
dx_x__ = 0.;
}
else
{
dx_x__ = hugeval;
}
dxrat = normdx / prevnormdx;
dzrat = dz_z__ / prev_dz_z__;
/* Check termination criteria. */
if (ymin * *rcond < incr_thresh__ * normy && y_prec_state__ < 2)
{
incr_prec__ = TRUE_;
}
if (x_state__ == 3 && dxrat <= *rthresh)
{
x_state__ = 1;
}
if (x_state__ == 1)
{
if (dx_x__ <= eps)
{
x_state__ = 2;
}
else if (dxrat > *rthresh)
{
if (y_prec_state__ != 2)
{
incr_prec__ = TRUE_;
}
else
{
x_state__ = 3;
}
}
else
{
if (dxrat > dxratmax)
{
dxratmax = dxrat;
}
}
if (x_state__ > 1)
{
final_dx_x__ = dx_x__;
}
}
if (z_state__ == 0 && dz_z__ <= *dz_ub__)
{
z_state__ = 1;
}
if (z_state__ == 3 && dzrat <= *rthresh)
{
z_state__ = 1;
}
if (z_state__ == 1)
{
if (dz_z__ <= eps)
{
z_state__ = 2;
}
else if (dz_z__ > *dz_ub__)
{
z_state__ = 0;
dzratmax = 0.;
final_dz_z__ = hugeval;
}
else if (dzrat > *rthresh)
{
if (y_prec_state__ != 2)
{
incr_prec__ = TRUE_;
}
else
{
z_state__ = 3;
}
}
else
{
if (dzrat > dzratmax)
{
dzratmax = dzrat;
}
}
if (z_state__ > 1)
{
final_dz_z__ = dz_z__;
}
}
if (x_state__ != 1 && (*ignore_cwise__ || z_state__ != 1))
{
goto L666;
}
if (incr_prec__)
{
incr_prec__ = FALSE_;
++y_prec_state__;
i__3 = *n;
for (i__ = 1;
i__ <= i__3;
++i__)
{
i__4 = i__;
y_tail__[i__4].r = 0.;
y_tail__[i__4].i = 0.; // , expr subst
}
}
prevnormdx = normdx;
prev_dz_z__ = dz_z__;
/* Update soluton. */
if (y_prec_state__ < 2)
{
zaxpy_(n, &c_b12, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1);
}
else
{
zla_wwaddw_(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]);
}
}
/* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't CALL F90_EXIT. */
L666: /* Set final_* when cnt hits ithresh. */
if (x_state__ == 1)
{
final_dx_x__ = dx_x__;
}
if (z_state__ == 1)
{
final_dz_z__ = dz_z__;
}
/* Compute error bounds. */
if (*n_norms__ >= 1)
{
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / ( 1 - dxratmax);
}
if (*n_norms__ >= 2)
{
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / ( 1 - dzratmax);
}
/* Compute componentwise relative backward error from formula */
/* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. */
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
zcopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
zhemv_(uplo, n, &c_b11, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, &c_b12, &res[1], &c__1);
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * b_dim1;
ayb[i__] = (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(&b[i__ + j * b_dim1]), abs(d__2));
}
/* Compute abs(op(A_s))*abs(Y) + abs(B_s). */
zla_heamv_(&uplo2, n, &c_b34, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, &c_b34, &ayb[1], &c__1);
zla_lin_berr_(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]);
/* End of loop for each RHS. */
}
return 0;
}