/* Subroutine */ int cpbsv_(char *uplo, integer *n, integer *kd, integer *
nrhs, complex *ab, integer *ldab, complex *b, integer *ldb, integer *
info)
{
/* System generated locals */
integer ab_dim1, ab_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *), cpbtrf_(
char *, integer *, integer *, complex *, integer *, integer *), cpbtrs_(char *, integer *, integer *, integer *, complex
*, integer *, complex *, integer *, integer *);
/* -- LAPACK driver routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CPBSV computes the solution to a complex system of linear equations */
/* A * X = B, */
/* where A is an N-by-N Hermitian positive definite band 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 band matrix, and L is a lower */
/* triangular band matrix, with the same number of superdiagonals or */
/* subdiagonals as A. 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. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrix B. NRHS >= 0. */
/* AB (input/output) COMPLEX array, dimension (LDAB,N) */
/* On entry, the upper or lower triangle of the Hermitian band */
/* matrix A, stored in the first KD+1 rows of the array. The */
/* j-th column of A is stored in the j-th column of the array AB */
/* as follows: */
/* if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). */
/* See below for further details. */
/* On exit, if INFO = 0, the triangular factor U or L from the */
/* Cholesky factorization A = U**H*U or A = L*L**H of the band */
/* matrix A, in the same storage format as A. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS right hand side matrix B. */
/* On exit, if INFO = 0, the N-by-NRHS solution matrix X. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, the leading minor of order i of A is not */
/* positive definite, so the factorization could not be */
/* completed, and the solution has not been computed. */
/* Further Details */
/* =============== */
/* The band storage scheme is illustrated by the following example, when */
/* N = 6, KD = 2, and UPLO = 'U': */
/* On entry: On exit: */
/* * * a13 a24 a35 a46 * * u13 u24 u35 u46 */
/* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 */
/* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 */
/* Similarly, if UPLO = 'L' the format of A is as follows: */
/* On entry: On exit: */
/* a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 */
/* a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * */
/* a31 a42 a53 a64 * * l31 l42 l53 l64 * * */
/* Array elements marked * are not used by the routine. */
/* ===================================================================== */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kd < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*ldab < *kd + 1) {
*info = -6;
} else if (*ldb < max(1,*n)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPBSV ", &i__1);
return 0;
}
/* Compute the Cholesky factorization A = U'*U or A = L*L'. */
cpbtrf_(uplo, n, kd, &ab[ab_offset], ldab, info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
cpbtrs_(uplo, n, kd, nrhs, &ab[ab_offset], ldab, &b[b_offset], ldb,
info);
}
return 0;
/* End of CPBSV */
} /* cpbsv_ */
/* Subroutine */ int cerrpo_(char *path, integer *nunit)
{
/* System generated locals */
integer i__1;
real r__1, r__2;
complex q__1;
/* Local variables */
complex a[16] /* was [4][4] */, b[4];
integer i__, j;
real r__[4];
complex w[8], x[4];
char c2[2];
real r1[4], r2[4];
complex af[16] /* was [4][4] */;
integer info;
real anrm, rcond;
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CERRPO tests the error exits for the COMPLEX routines */
/* for Hermitian positive definite matrices. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Set the variables to innocuous values. */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
i__1 = i__ + (j << 2) - 5;
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = i__ + (j << 2) - 5;
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
af[i__1].r = q__1.r, af[i__1].i = q__1.i;
/* L10: */
}
i__1 = j - 1;
b[i__1].r = 0.f, b[i__1].i = 0.f;
r1[j - 1] = 0.f;
r2[j - 1] = 0.f;
i__1 = j - 1;
w[i__1].r = 0.f, w[i__1].i = 0.f;
i__1 = j - 1;
x[i__1].r = 0.f, x[i__1].i = 0.f;
/* L20: */
}
anrm = 1.f;
infoc_1.ok = TRUE_;
/* Test error exits of the routines that use the Cholesky */
/* decomposition of a Hermitian positive definite matrix. */
if (lsamen_(&c__2, c2, "PO")) {
/* CPOTRF */
s_copy(srnamc_1.srnamt, "CPOTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpotrf_("/", &c__0, a, &c__1, &info);
chkxer_("CPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpotrf_("U", &c_n1, a, &c__1, &info);
chkxer_("CPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cpotrf_("U", &c__2, a, &c__1, &info);
chkxer_("CPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPOTF2 */
s_copy(srnamc_1.srnamt, "CPOTF2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpotf2_("/", &c__0, a, &c__1, &info);
chkxer_("CPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpotf2_("U", &c_n1, a, &c__1, &info);
chkxer_("CPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cpotf2_("U", &c__2, a, &c__1, &info);
chkxer_("CPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPOTRI */
s_copy(srnamc_1.srnamt, "CPOTRI", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpotri_("/", &c__0, a, &c__1, &info);
chkxer_("CPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpotri_("U", &c_n1, a, &c__1, &info);
chkxer_("CPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cpotri_("U", &c__2, a, &c__1, &info);
chkxer_("CPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPOTRS */
s_copy(srnamc_1.srnamt, "CPOTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpotrs_("/", &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("CPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpotrs_("U", &c_n1, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("CPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpotrs_("U", &c__0, &c_n1, a, &c__1, b, &c__1, &info);
chkxer_("CPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cpotrs_("U", &c__2, &c__1, a, &c__1, b, &c__2, &info);
chkxer_("CPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cpotrs_("U", &c__2, &c__1, a, &c__2, b, &c__1, &info);
chkxer_("CPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPORFS */
s_copy(srnamc_1.srnamt, "CPORFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cporfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cporfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cporfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cporfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &c__2,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cporfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &c__2,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
cporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__1, x, &c__2,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
cporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__2, x, &c__1,
r1, r2, w, r__, &info);
chkxer_("CPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPOCON */
s_copy(srnamc_1.srnamt, "CPOCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpocon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("CPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpocon_("U", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("CPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cpocon_("U", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("CPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
r__1 = -anrm;
cpocon_("U", &c__1, a, &c__1, &r__1, &rcond, w, r__, &info)
;
chkxer_("CPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPOEQU */
s_copy(srnamc_1.srnamt, "CPOEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpoequ_(&c_n1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("CPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpoequ_(&c__2, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("CPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Test error exits of the routines that use the Cholesky */
/* decomposition of a Hermitian positive definite packed matrix. */
} else if (lsamen_(&c__2, c2, "PP")) {
/* CPPTRF */
s_copy(srnamc_1.srnamt, "CPPTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpptrf_("/", &c__0, a, &info);
chkxer_("CPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpptrf_("U", &c_n1, a, &info);
chkxer_("CPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPPTRI */
s_copy(srnamc_1.srnamt, "CPPTRI", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpptri_("/", &c__0, a, &info);
chkxer_("CPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpptri_("U", &c_n1, a, &info);
chkxer_("CPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPPTRS */
s_copy(srnamc_1.srnamt, "CPPTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpptrs_("/", &c__0, &c__0, a, b, &c__1, &info);
chkxer_("CPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpptrs_("U", &c_n1, &c__0, a, b, &c__1, &info);
chkxer_("CPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpptrs_("U", &c__0, &c_n1, a, b, &c__1, &info);
chkxer_("CPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
cpptrs_("U", &c__2, &c__1, a, b, &c__1, &info);
chkxer_("CPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPPRFS */
s_copy(srnamc_1.srnamt, "CPPRFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpprfs_("/", &c__0, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("CPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpprfs_("U", &c_n1, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("CPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpprfs_("U", &c__0, &c_n1, a, af, b, &c__1, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("CPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cpprfs_("U", &c__2, &c__1, a, af, b, &c__1, x, &c__2, r1, r2, w, r__,
&info);
chkxer_("CPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
cpprfs_("U", &c__2, &c__1, a, af, b, &c__2, x, &c__1, r1, r2, w, r__,
&info);
chkxer_("CPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPPCON */
s_copy(srnamc_1.srnamt, "CPPCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cppcon_("/", &c__0, a, &anrm, &rcond, w, r__, &info);
chkxer_("CPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cppcon_("U", &c_n1, a, &anrm, &rcond, w, r__, &info);
chkxer_("CPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
r__1 = -anrm;
cppcon_("U", &c__1, a, &r__1, &rcond, w, r__, &info);
chkxer_("CPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPPEQU */
s_copy(srnamc_1.srnamt, "CPPEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cppequ_("/", &c__0, a, r1, &rcond, &anrm, &info);
chkxer_("CPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cppequ_("U", &c_n1, a, r1, &rcond, &anrm, &info);
chkxer_("CPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Test error exits of the routines that use the Cholesky */
/* decomposition of a Hermitian positive definite band matrix. */
} else if (lsamen_(&c__2, c2, "PB")) {
/* CPBTRF */
s_copy(srnamc_1.srnamt, "CPBTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpbtrf_("/", &c__0, &c__0, a, &c__1, &info);
chkxer_("CPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpbtrf_("U", &c_n1, &c__0, a, &c__1, &info);
chkxer_("CPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpbtrf_("U", &c__1, &c_n1, a, &c__1, &info);
chkxer_("CPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cpbtrf_("U", &c__2, &c__1, a, &c__1, &info);
chkxer_("CPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPBTF2 */
s_copy(srnamc_1.srnamt, "CPBTF2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpbtf2_("/", &c__0, &c__0, a, &c__1, &info);
chkxer_("CPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpbtf2_("U", &c_n1, &c__0, a, &c__1, &info);
chkxer_("CPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpbtf2_("U", &c__1, &c_n1, a, &c__1, &info);
chkxer_("CPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cpbtf2_("U", &c__2, &c__1, a, &c__1, &info);
chkxer_("CPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPBTRS */
s_copy(srnamc_1.srnamt, "CPBTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpbtrs_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("CPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpbtrs_("U", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("CPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpbtrs_("U", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("CPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cpbtrs_("U", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, &info);
chkxer_("CPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
cpbtrs_("U", &c__2, &c__1, &c__1, a, &c__1, b, &c__1, &info);
chkxer_("CPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cpbtrs_("U", &c__2, &c__0, &c__1, a, &c__1, b, &c__1, &info);
chkxer_("CPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPBRFS */
s_copy(srnamc_1.srnamt, "CPBRFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpbrfs_("/", &c__0, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpbrfs_("U", &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpbrfs_("U", &c__1, &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cpbrfs_("U", &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
cpbrfs_("U", &c__2, &c__1, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cpbrfs_("U", &c__2, &c__1, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__1, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__2, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPBCON */
s_copy(srnamc_1.srnamt, "CPBCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpbcon_("/", &c__0, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("CPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpbcon_("U", &c_n1, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("CPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpbcon_("U", &c__1, &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("CPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cpbcon_("U", &c__2, &c__1, a, &c__1, &anrm, &rcond, w, r__, &info);
chkxer_("CPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
r__1 = -anrm;
cpbcon_("U", &c__1, &c__0, a, &c__1, &r__1, &rcond, w, r__, &info);
chkxer_("CPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CPBEQU */
s_copy(srnamc_1.srnamt, "CPBEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cpbequ_("/", &c__0, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("CPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cpbequ_("U", &c_n1, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("CPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cpbequ_("U", &c__1, &c_n1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("CPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cpbequ_("U", &c__2, &c__1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("CPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
}
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of CERRPO */
} /* cerrpo_ */
/* Subroutine */ int cdrvpb_(logical *dotype, integer *nn, integer *nval,
integer *nrhs, real *thresh, logical *tsterr, integer *nmax, complex *
a, complex *afac, complex *asav, complex *b, complex *bsav, complex *
x, complex *xact, real *s, complex *work, real *rwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char facts[1*3] = "F" "N" "E";
static char equeds[1*2] = "N" "Y";
/* Format strings */
static char fmt_9999[] = "(1x,a6,\002, UPLO='\002,a1,\002', N =\002,i5"
",\002, KD =\002,i5,\002, type \002,i1,\002, test(\002,i1,\002)"
"=\002,g12.5)";
static char fmt_9997[] = "(1x,a6,\002( '\002,a1,\002', '\002,a1,\002',"
" \002,i5,\002, \002,i5,\002, ... ), EQUED='\002,a1,\002', type"
" \002,i1,\002, test(\002,i1,\002)=\002,g12.5)";
static char fmt_9998[] = "(1x,a6,\002( '\002,a1,\002', '\002,a1,\002',"
" \002,i5,\002, \002,i5,\002, ... ), type \002,i1,\002, test(\002"
",i1,\002)=\002,g12.5)";
/* System generated locals */
address a__1[2];
integer i__1, i__2, i__3, i__4, i__5, i__6, i__7[2];
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
integer i__, k, n, i1, i2, k1, kd, nb, in, kl, iw, ku, nt, lda, ikd, nkd,
ldab;
char fact[1];
integer ioff, mode, koff;
real amax;
char path[3];
integer imat, info;
char dist[1], uplo[1], type__[1];
integer nrun, ifact;
extern /* Subroutine */ int cget04_(integer *, integer *, complex *,
integer *, complex *, integer *, real *, real *);
integer nfail, iseed[4], nfact;
extern /* Subroutine */ int cpbt01_(char *, integer *, integer *, complex
*, integer *, complex *, integer *, real *, real *),
cpbt02_(char *, integer *, integer *, integer *, complex *,
integer *, complex *, integer *, complex *, integer *, real *,
real *), cpbt05_(char *, integer *, integer *, integer *,
complex *, integer *, complex *, integer *, complex *, integer *,
complex *, integer *, real *, real *, real *);
integer kdval[4];
extern logical lsame_(char *, char *);
char equed[1];
integer nbmin;
real rcond, roldc, scond;
integer nimat;
extern doublereal sget06_(real *, real *);
real anorm;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), cpbsv_(char *, integer *, integer *,
integer *, complex *, integer *, complex *, integer *, integer *);
logical equil;
extern /* Subroutine */ int cswap_(integer *, complex *, integer *,
complex *, integer *);
integer iuplo, izero, nerrs;
logical zerot;
char xtype[1];
extern /* Subroutine */ int clatb4_(char *, integer *, integer *, integer
*, char *, integer *, integer *, real *, integer *, real *, char *
), aladhd_(integer *, char *);
extern doublereal clanhb_(char *, char *, integer *, integer *, complex *,
integer *, real *), clange_(char *, integer *,
integer *, complex *, integer *, real *);
extern /* Subroutine */ int claqhb_(char *, integer *, integer *, complex
*, integer *, real *, real *, real *, char *),
alaerh_(char *, char *, integer *, integer *, char *, integer *,
integer *, integer *, integer *, integer *, integer *, integer *,
integer *, integer *), claipd_(integer *,
complex *, integer *, integer *);
logical prefac;
real rcondc;
logical nofact;
char packit[1];
integer iequed;
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), clarhs_(char *, char
*, char *, char *, integer *, integer *, integer *, integer *,
integer *, complex *, integer *, complex *, integer *, complex *,
integer *, integer *, integer *),
claset_(char *, integer *, integer *, complex *, complex *,
complex *, integer *), cpbequ_(char *, integer *, integer
*, complex *, integer *, real *, real *, real *, integer *), alasvm_(char *, integer *, integer *, integer *, integer
*);
real cndnum;
extern /* Subroutine */ int clatms_(integer *, integer *, char *, integer
*, char *, real *, integer *, real *, real *, integer *, integer *
, char *, complex *, integer *, complex *, integer *), cpbtrf_(char *, integer *, integer *, complex *,
integer *, integer *);
real ainvnm;
extern /* Subroutine */ int cpbtrs_(char *, integer *, integer *, integer
*, complex *, integer *, complex *, integer *, integer *),
xlaenv_(integer *, integer *), cpbsvx_(char *, char *, integer *,
integer *, integer *, complex *, integer *, complex *, integer *,
char *, real *, complex *, integer *, complex *, integer *, real
*, real *, real *, complex *, real *, integer *), cerrvx_(char *, integer *);
real result[6];
/* Fortran I/O blocks */
static cilist io___57 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___60 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___61 = { 0, 0, 0, fmt_9998, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CDRVPB tests the driver routines CPBSV and -SVX. */
/* Arguments */
/* ========= */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* The matrix types to be used for testing. Matrices of type j */
/* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix dimension N. */
/* NRHS (input) INTEGER */
/* The number of right hand side vectors to be generated for */
/* each linear system. */
/* THRESH (input) REAL */
/* 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 array, dimension (NMAX*NMAX) */
/* AFAC (workspace) COMPLEX array, dimension (NMAX*NMAX) */
/* ASAV (workspace) COMPLEX array, dimension (NMAX*NMAX) */
/* B (workspace) COMPLEX array, dimension (NMAX*NRHS) */
/* BSAV (workspace) COMPLEX array, dimension (NMAX*NRHS) */
/* X (workspace) COMPLEX array, dimension (NMAX*NRHS) */
/* XACT (workspace) COMPLEX array, dimension (NMAX*NRHS) */
/* S (workspace) REAL array, dimension (NMAX) */
/* WORK (workspace) COMPLEX array, dimension */
/* (NMAX*max(3,NRHS)) */
/* RWORK (workspace) REAL array, dimension (NMAX+2*NRHS) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--rwork;
--work;
--s;
--xact;
--x;
--bsav;
--b;
--asav;
--afac;
--a;
--nval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Complex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "PB", (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) {
cerrvx_(path, nout);
}
infoc_1.infot = 0;
kdval[0] = 0;
/* Set the block size and minimum block size for testing. */
nb = 1;
nbmin = 2;
xlaenv_(&c__1, &nb);
xlaenv_(&c__2, &nbmin);
/* 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';
/* Set limits on the number of loop iterations. */
/* Computing MAX */
i__2 = 1, i__3 = min(n,4);
nkd = max(i__2,i__3);
nimat = 8;
if (n == 0) {
nimat = 1;
}
kdval[1] = n + (n + 1) / 4;
kdval[2] = (n * 3 - 1) / 4;
kdval[3] = (n + 1) / 4;
i__2 = nkd;
for (ikd = 1; ikd <= i__2; ++ikd) {
/* Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order */
/* makes it easier to skip redundant values for small values */
/* of N. */
kd = kdval[ikd - 1];
ldab = kd + 1;
/* Do first for UPLO = 'U', then for UPLO = 'L' */
for (iuplo = 1; iuplo <= 2; ++iuplo) {
koff = 1;
if (iuplo == 1) {
*(unsigned char *)uplo = 'U';
*(unsigned char *)packit = 'Q';
/* Computing MAX */
i__3 = 1, i__4 = kd + 2 - n;
koff = max(i__3,i__4);
} else {
*(unsigned char *)uplo = 'L';
*(unsigned char *)packit = 'B';
}
i__3 = nimat;
for (imat = 1; imat <= i__3; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L80;
}
/* Skip types 2, 3, or 4 if the matrix size is too small. */
zerot = imat >= 2 && imat <= 4;
if (zerot && n < imat - 1) {
goto L80;
}
if (! zerot || ! dotype[1]) {
/* Set up parameters with CLATB4 and generate a test */
/* matrix with CLATMS. */
clatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm,
&mode, &cndnum, dist);
s_copy(srnamc_1.srnamt, "CLATMS", (ftnlen)6, (ftnlen)
6);
clatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode,
&cndnum, &anorm, &kd, &kd, packit, &a[koff],
&ldab, &work[1], &info);
/* Check error code from CLATMS. */
if (info != 0) {
alaerh_(path, "CLATMS", &info, &c__0, uplo, &n, &
n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &
nerrs, nout);
goto L80;
}
} else if (izero > 0) {
/* Use the same matrix for types 3 and 4 as for type */
/* 2 by copying back the zeroed out column, */
iw = (lda << 1) + 1;
if (iuplo == 1) {
ioff = (izero - 1) * ldab + kd + 1;
i__4 = izero - i1;
ccopy_(&i__4, &work[iw], &c__1, &a[ioff - izero +
i1], &c__1);
iw = iw + izero - i1;
i__4 = i2 - izero + 1;
/* Computing MAX */
i__6 = ldab - 1;
i__5 = max(i__6,1);
ccopy_(&i__4, &work[iw], &c__1, &a[ioff], &i__5);
} else {
ioff = (i1 - 1) * ldab + 1;
i__4 = izero - i1;
/* Computing MAX */
i__6 = ldab - 1;
i__5 = max(i__6,1);
ccopy_(&i__4, &work[iw], &c__1, &a[ioff + izero -
i1], &i__5);
ioff = (izero - 1) * ldab + 1;
iw = iw + izero - i1;
i__4 = i2 - izero + 1;
ccopy_(&i__4, &work[iw], &c__1, &a[ioff], &c__1);
}
}
/* For types 2-4, zero one row and column of the matrix */
/* to test that INFO is returned correctly. */
izero = 0;
if (zerot) {
if (imat == 2) {
izero = 1;
} else if (imat == 3) {
izero = n;
} else {
izero = n / 2 + 1;
}
/* Save the zeroed out row and column in WORK(*,3) */
iw = lda << 1;
/* Computing MIN */
i__5 = (kd << 1) + 1;
i__4 = min(i__5,n);
for (i__ = 1; i__ <= i__4; ++i__) {
i__5 = iw + i__;
work[i__5].r = 0.f, work[i__5].i = 0.f;
/* L20: */
}
++iw;
/* Computing MAX */
i__4 = izero - kd;
i1 = max(i__4,1);
/* Computing MIN */
i__4 = izero + kd;
i2 = min(i__4,n);
if (iuplo == 1) {
ioff = (izero - 1) * ldab + kd + 1;
i__4 = izero - i1;
cswap_(&i__4, &a[ioff - izero + i1], &c__1, &work[
iw], &c__1);
iw = iw + izero - i1;
i__4 = i2 - izero + 1;
/* Computing MAX */
i__6 = ldab - 1;
i__5 = max(i__6,1);
cswap_(&i__4, &a[ioff], &i__5, &work[iw], &c__1);
} else {
ioff = (i1 - 1) * ldab + 1;
i__4 = izero - i1;
/* Computing MAX */
i__6 = ldab - 1;
i__5 = max(i__6,1);
cswap_(&i__4, &a[ioff + izero - i1], &i__5, &work[
iw], &c__1);
ioff = (izero - 1) * ldab + 1;
iw = iw + izero - i1;
i__4 = i2 - izero + 1;
cswap_(&i__4, &a[ioff], &c__1, &work[iw], &c__1);
}
}
/* Set the imaginary part of the diagonals. */
if (iuplo == 1) {
claipd_(&n, &a[kd + 1], &ldab, &c__0);
} else {
claipd_(&n, &a[1], &ldab, &c__0);
}
/* Save a copy of the matrix A in ASAV. */
i__4 = kd + 1;
clacpy_("Full", &i__4, &n, &a[1], &ldab, &asav[1], &ldab);
for (iequed = 1; iequed <= 2; ++iequed) {
*(unsigned char *)equed = *(unsigned char *)&equeds[
iequed - 1];
if (iequed == 1) {
nfact = 3;
} else {
nfact = 1;
}
i__4 = nfact;
for (ifact = 1; ifact <= i__4; ++ifact) {
*(unsigned char *)fact = *(unsigned char *)&facts[
ifact - 1];
prefac = lsame_(fact, "F");
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
if (zerot) {
if (prefac) {
goto L60;
}
rcondc = 0.f;
} else if (! lsame_(fact, "N")) {
/* Compute the condition number for comparison */
/* with the value returned by CPBSVX (FACT = */
/* 'N' reuses the condition number from the */
/* previous iteration with FACT = 'F'). */
i__5 = kd + 1;
clacpy_("Full", &i__5, &n, &asav[1], &ldab, &
afac[1], &ldab);
if (equil || iequed > 1) {
/* Compute row and column scale factors to */
/* equilibrate the matrix A. */
cpbequ_(uplo, &n, &kd, &afac[1], &ldab, &
s[1], &scond, &amax, &info);
if (info == 0 && n > 0) {
if (iequed > 1) {
scond = 0.f;
}
/* Equilibrate the matrix. */
claqhb_(uplo, &n, &kd, &afac[1], &
ldab, &s[1], &scond, &amax,
equed);
}
}
/* Save the condition number of the */
/* non-equilibrated system for use in CGET04. */
if (equil) {
roldc = rcondc;
}
/* Compute the 1-norm of A. */
anorm = clanhb_("1", uplo, &n, &kd, &afac[1],
&ldab, &rwork[1]);
/* Factor the matrix A. */
cpbtrf_(uplo, &n, &kd, &afac[1], &ldab, &info);
/* Form the inverse of A. */
claset_("Full", &n, &n, &c_b47, &c_b48, &a[1],
&lda);
s_copy(srnamc_1.srnamt, "CPBTRS", (ftnlen)6, (
ftnlen)6);
cpbtrs_(uplo, &n, &kd, &n, &afac[1], &ldab, &
a[1], &lda, &info);
/* Compute the 1-norm condition number of A. */
ainvnm = clange_("1", &n, &n, &a[1], &lda, &
rwork[1]);
if (anorm <= 0.f || ainvnm <= 0.f) {
rcondc = 1.f;
} else {
rcondc = 1.f / anorm / ainvnm;
}
}
/* Restore the matrix A. */
i__5 = kd + 1;
clacpy_("Full", &i__5, &n, &asav[1], &ldab, &a[1],
&ldab);
/* Form an exact solution and set the right hand */
/* side. */
s_copy(srnamc_1.srnamt, "CLARHS", (ftnlen)6, (
ftnlen)6);
clarhs_(path, xtype, uplo, " ", &n, &n, &kd, &kd,
nrhs, &a[1], &ldab, &xact[1], &lda, &b[1],
&lda, iseed, &info);
*(unsigned char *)xtype = 'C';
clacpy_("Full", &n, nrhs, &b[1], &lda, &bsav[1], &
lda);
if (nofact) {
/* --- Test CPBSV --- */
/* Compute the L*L' or U'*U factorization of the */
/* matrix and solve the system. */
i__5 = kd + 1;
clacpy_("Full", &i__5, &n, &a[1], &ldab, &
afac[1], &ldab);
clacpy_("Full", &n, nrhs, &b[1], &lda, &x[1],
&lda);
s_copy(srnamc_1.srnamt, "CPBSV ", (ftnlen)6, (
ftnlen)6);
cpbsv_(uplo, &n, &kd, nrhs, &afac[1], &ldab, &
x[1], &lda, &info);
/* Check error code from CPBSV . */
if (info != izero) {
alaerh_(path, "CPBSV ", &info, &izero,
uplo, &n, &n, &kd, &kd, nrhs, &
imat, &nfail, &nerrs, nout);
goto L40;
} else if (info != 0) {
goto L40;
}
/* Reconstruct matrix from factors and compute */
/* residual. */
cpbt01_(uplo, &n, &kd, &a[1], &ldab, &afac[1],
&ldab, &rwork[1], result);
/* Compute residual of the computed solution. */
clacpy_("Full", &n, nrhs, &b[1], &lda, &work[
1], &lda);
cpbt02_(uplo, &n, &kd, nrhs, &a[1], &ldab, &x[
1], &lda, &work[1], &lda, &rwork[1], &
result[1]);
/* Check solution from generated exact solution. */
cget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda,
&rcondc, &result[2]);
nt = 3;
/* Print information about the tests that did */
/* not pass the threshold. */
i__5 = nt;
for (k = 1; k <= i__5; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
io___57.ciunit = *nout;
s_wsfe(&io___57);
do_fio(&c__1, "CPBSV ", (ftnlen)6);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&kd, (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(real));
e_wsfe();
++nfail;
}
/* L30: */
}
nrun += nt;
L40:
;
}
/* --- Test CPBSVX --- */
if (! prefac) {
i__5 = kd + 1;
claset_("Full", &i__5, &n, &c_b47, &c_b47, &
afac[1], &ldab);
}
claset_("Full", &n, nrhs, &c_b47, &c_b47, &x[1], &
lda);
if (iequed > 1 && n > 0) {
/* Equilibrate the matrix if FACT='F' and */
/* EQUED='Y' */
claqhb_(uplo, &n, &kd, &a[1], &ldab, &s[1], &
scond, &amax, equed);
}
/* Solve the system and compute the condition */
/* number and error bounds using CPBSVX. */
s_copy(srnamc_1.srnamt, "CPBSVX", (ftnlen)6, (
ftnlen)6);
cpbsvx_(fact, uplo, &n, &kd, nrhs, &a[1], &ldab, &
afac[1], &ldab, equed, &s[1], &b[1], &lda,
&x[1], &lda, &rcond, &rwork[1], &rwork[*
nrhs + 1], &work[1], &rwork[(*nrhs << 1)
+ 1], &info);
/* Check the error code from CPBSVX. */
if (info != izero) {
/* Writing concatenation */
i__7[0] = 1, a__1[0] = fact;
i__7[1] = 1, a__1[1] = uplo;
s_cat(ch__1, a__1, i__7, &c__2, (ftnlen)2);
alaerh_(path, "CPBSVX", &info, &izero, ch__1,
&n, &n, &kd, &kd, nrhs, &imat, &nfail,
&nerrs, nout);
goto L60;
}
if (info == 0) {
if (! prefac) {
/* Reconstruct matrix from factors and */
/* compute residual. */
cpbt01_(uplo, &n, &kd, &a[1], &ldab, &
afac[1], &ldab, &rwork[(*nrhs <<
1) + 1], result);
k1 = 1;
} else {
k1 = 2;
}
/* Compute residual of the computed solution. */
clacpy_("Full", &n, nrhs, &bsav[1], &lda, &
work[1], &lda);
cpbt02_(uplo, &n, &kd, nrhs, &asav[1], &ldab,
&x[1], &lda, &work[1], &lda, &rwork[(*
nrhs << 1) + 1], &result[1]);
/* Check solution from generated exact solution. */
if (nofact || prefac && lsame_(equed, "N")) {
cget04_(&n, nrhs, &x[1], &lda, &xact[1], &
lda, &rcondc, &result[2]);
} else {
cget04_(&n, nrhs, &x[1], &lda, &xact[1], &
lda, &roldc, &result[2]);
}
/* Check the error bounds from iterative */
/* refinement. */
cpbt05_(uplo, &n, &kd, nrhs, &asav[1], &ldab,
&b[1], &lda, &x[1], &lda, &xact[1], &
lda, &rwork[1], &rwork[*nrhs + 1], &
result[3]);
} else {
k1 = 6;
}
/* Compare RCOND from CPBSVX with the computed */
/* value in RCONDC. */
result[5] = sget06_(&rcond, &rcondc);
/* Print information about the tests that did not */
/* pass the threshold. */
for (k = k1; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___60.ciunit = *nout;
s_wsfe(&io___60);
do_fio(&c__1, "CPBSVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&kd, (ftnlen)
sizeof(integer));
do_fio(&c__1, equed, (ftnlen)1);
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(real));
e_wsfe();
} else {
io___61.ciunit = *nout;
s_wsfe(&io___61);
do_fio(&c__1, "CPBSVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&kd, (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(real));
e_wsfe();
}
++nfail;
}
/* L50: */
}
nrun = nrun + 7 - k1;
L60:
;
}
/* L70: */
}
L80:
;
}
/* L90: */
}
/* L100: */
}
/* L110: */
}
/* Print a summary of the results. */
alasvm_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of CDRVPB */
} /* cdrvpb_ */
/* Subroutine */
int cpbsvx_(char *fact, char *uplo, integer *n, integer *kd, integer *nrhs, complex *ab, integer *ldab, complex *afb, integer * ldafb, char *equed, real *s, complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, real *ferr, real *berr, complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2;
complex q__1;
/* Local variables */
integer i__, j, j1, j2;
real amax, smin, smax;
extern logical lsame_(char *, char *);
real scond, anorm;
extern /* Subroutine */
int ccopy_(integer *, complex *, integer *, complex *, integer *);
logical equil, rcequ, upper;
extern real clanhb_(char *, char *, integer *, integer *, complex *, integer *, real *);
extern /* Subroutine */
int claqhb_(char *, integer *, integer *, complex *, integer *, real *, real *, real *, char *), cpbcon_(char *, integer *, integer *, complex *, integer *, real * , real *, complex *, real *, integer *);
extern real slamch_(char *);
logical nofact;
extern /* Subroutine */
int clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *), cpbequ_(char *, integer *, integer *, complex *, integer *, real *, real *, real *, integer *), cpbrfs_( char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, real *, real *, complex *, real *, integer *);
real bignum;
extern /* Subroutine */
int cpbtrf_(char *, integer *, integer *, complex *, integer *, integer *);
integer infequ;
extern /* Subroutine */
int cpbtrs_(char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, integer *);
real smlnum;
/* -- 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 */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
afb_dim1 = *ldafb;
afb_offset = 1 + afb_dim1;
afb -= afb_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");
upper = lsame_(uplo, "U");
if (nofact || equil)
{
*(unsigned char *)equed = 'N';
rcequ = FALSE_;
}
else
{
rcequ = lsame_(equed, "Y");
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
}
/* Test the input parameters. */
if (! nofact && ! equil && ! lsame_(fact, "F"))
{
*info = -1;
}
else if (! upper && ! lsame_(uplo, "L"))
{
*info = -2;
}
else if (*n < 0)
{
*info = -3;
}
else if (*kd < 0)
{
*info = -4;
}
else if (*nrhs < 0)
{
*info = -5;
}
else if (*ldab < *kd + 1)
{
*info = -7;
}
else if (*ldafb < *kd + 1)
{
*info = -9;
}
else if (lsame_(fact, "F") && ! (rcequ || lsame_( equed, "N")))
{
*info = -10;
}
else
{
if (rcequ)
{
smin = bignum;
smax = 0.f;
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
/* Computing MIN */
r__1 = smin;
r__2 = s[j]; // , expr subst
smin = min(r__1,r__2);
/* Computing MAX */
r__1 = smax;
r__2 = s[j]; // , expr subst
smax = max(r__1,r__2);
/* L10: */
}
if (smin <= 0.f)
{
*info = -11;
}
else if (*n > 0)
{
scond = max(smin,smlnum) / min(smax,bignum);
}
else
{
scond = 1.f;
}
}
if (*info == 0)
{
if (*ldb < max(1,*n))
{
*info = -13;
}
else if (*ldx < max(1,*n))
{
*info = -15;
}
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CPBSVX", &i__1);
return 0;
}
if (equil)
{
/* Compute row and column scalings to equilibrate the matrix A. */
cpbequ_(uplo, n, kd, &ab[ab_offset], ldab, &s[1], &scond, &amax, & infequ);
if (infequ == 0)
{
/* Equilibrate the matrix. */
claqhb_(uplo, n, kd, &ab[ab_offset], ldab, &s[1], &scond, &amax, equed);
rcequ = lsame_(equed, "Y");
}
}
/* Scale the right-hand side. */
if (rcequ)
{
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * b_dim1;
i__4 = i__;
i__5 = i__ + j * b_dim1;
q__1.r = s[i__4] * b[i__5].r;
q__1.i = s[i__4] * b[i__5].i; // , expr subst
b[i__3].r = q__1.r;
b[i__3].i = q__1.i; // , expr subst
/* L20: */
}
/* L30: */
}
}
if (nofact || equil)
{
/* Compute the Cholesky factorization A = U**H *U or A = L*L**H. */
if (upper)
{
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
/* Computing MAX */
i__2 = j - *kd;
j1 = max(i__2,1);
i__2 = j - j1 + 1;
ccopy_(&i__2, &ab[*kd + 1 - j + j1 + j * ab_dim1], &c__1, & afb[*kd + 1 - j + j1 + j * afb_dim1], &c__1);
/* L40: */
}
}
else
{
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
/* Computing MIN */
i__2 = j + *kd;
j2 = min(i__2,*n);
i__2 = j2 - j + 1;
ccopy_(&i__2, &ab[j * ab_dim1 + 1], &c__1, &afb[j * afb_dim1 + 1], &c__1);
/* L50: */
}
}
cpbtrf_(uplo, n, kd, &afb[afb_offset], ldafb, info);
/* Return if INFO is non-zero. */
if (*info > 0)
{
*rcond = 0.f;
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = clanhb_("1", uplo, n, kd, &ab[ab_offset], ldab, &rwork[1]);
/* Compute the reciprocal of the condition number of A. */
cpbcon_(uplo, n, kd, &afb[afb_offset], ldafb, &anorm, rcond, &work[1], & rwork[1], info);
/* Compute the solution matrix X. */
clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
cpbtrs_(uplo, n, kd, nrhs, &afb[afb_offset], ldafb, &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
cpbrfs_(uplo, n, kd, nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1] , &rwork[1], info);
/* Transform the solution matrix X to a solution of the original */
/* system. */
if (rcequ)
{
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * x_dim1;
i__4 = i__;
i__5 = i__ + j * x_dim1;
q__1.r = s[i__4] * x[i__5].r;
q__1.i = s[i__4] * x[i__5].i; // , expr subst
x[i__3].r = q__1.r;
x[i__3].i = q__1.i; // , expr subst
/* L60: */
}
/* L70: */
}
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
ferr[j] /= scond;
/* L80: */
}
}
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon"))
{
*info = *n + 1;
}
return 0;
/* End of CPBSVX */
}
/* Subroutine */ int cchkpb_(logical *dotype, integer *nn, integer *nval,
integer *nnb, integer *nbval, integer *nns, integer *nsval, real *
thresh, logical *tsterr, integer *nmax, complex *a, complex *afac,
complex *ainv, complex *b, complex *x, complex *xact, complex *work,
real *rwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
/* Format strings */
static char fmt_9999[] = "(\002 UPLO='\002,a1,\002', N=\002,i5,\002, KD"
"=\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, KD"
"=\002,i5,\002, NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i"
"2,\002) = \002,g12.5)";
static char fmt_9997[] = "(\002 UPLO='\002,a1,\002', N=\002,i5,\002, KD"
"=\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, i__5, i__6;
/* Local variables */
integer i__, k, n, i1, i2, kd, nb, in, kl, iw, ku, lda, ikd, inb, nkd,
ldab, ioff, mode, koff, imat, info;
char path[3], dist[1];
integer irhs, nrhs;
char uplo[1], type__[1];
integer nrun;
integer nfail, iseed[4];
integer kdval[4];
real rcond;
integer nimat;
real anorm;
integer iuplo, izero, nerrs;
logical zerot;
char xtype[1];
real rcondc;
char packit[1];
real cndnum;
real ainvnm;
real result[7];
/* Fortran I/O blocks */
static cilist io___40 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___46 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___48 = { 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 */
/* ======= */
/* CCHKPB tests CPBTRF, -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) REAL */
/* 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) REAL array, dimension (NMAX*NMAX) */
/* AFAC (workspace) REAL array, dimension (NMAX*NMAX) */
/* AINV (workspace) REAL array, dimension (NMAX*NMAX) */
/* B (workspace) REAL array, dimension (NMAX*NSMAX) */
/* where NSMAX is the largest entry in NSVAL. */
/* X (workspace) REAL array, dimension (NMAX*NSMAX) */
/* XACT (workspace) REAL array, dimension (NMAX*NSMAX) */
/* WORK (workspace) REAL array, dimension */
/* (NMAX*max(3,NSMAX)) */
/* RWORK (workspace) REAL array, dimension */
/* (max(NMAX,2*NSMAX)) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--rwork;
--work;
--xact;
--x;
--b;
--ainv;
--afac;
--a;
--nsval;
--nbval;
--nval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Complex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "PB", (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) {
cerrpo_(path, nout);
}
infoc_1.infot = 0;
kdval[0] = 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';
/* Set limits on the number of loop iterations. */
/* Computing MAX */
i__2 = 1, i__3 = min(n,4);
nkd = max(i__2,i__3);
nimat = 8;
if (n == 0) {
nimat = 1;
}
kdval[1] = n + (n + 1) / 4;
kdval[2] = (n * 3 - 1) / 4;
kdval[3] = (n + 1) / 4;
i__2 = nkd;
for (ikd = 1; ikd <= i__2; ++ikd) {
/* Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order */
/* makes it easier to skip redundant values for small values */
/* of N. */
kd = kdval[ikd - 1];
ldab = kd + 1;
/* Do first for UPLO = 'U', then for UPLO = 'L' */
for (iuplo = 1; iuplo <= 2; ++iuplo) {
koff = 1;
if (iuplo == 1) {
*(unsigned char *)uplo = 'U';
/* Computing MAX */
i__3 = 1, i__4 = kd + 2 - n;
koff = max(i__3,i__4);
*(unsigned char *)packit = 'Q';
} else {
*(unsigned char *)uplo = 'L';
*(unsigned char *)packit = 'B';
}
i__3 = nimat;
for (imat = 1; imat <= i__3; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L60;
}
/* Skip types 2, 3, or 4 if the matrix size is too small. */
zerot = imat >= 2 && imat <= 4;
if (zerot && n < imat - 1) {
goto L60;
}
if (! zerot || ! dotype[1]) {
/* Set up parameters with CLATB4 and generate a test */
/* matrix with CLATMS. */
clatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm,
&mode, &cndnum, dist);
s_copy(srnamc_1.srnamt, "CLATMS", (ftnlen)32, (ftnlen)
6);
clatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode,
&cndnum, &anorm, &kd, &kd, packit, &a[koff],
&ldab, &work[1], &info);
/* Check error code from CLATMS. */
if (info != 0) {
alaerh_(path, "CLATMS", &info, &c__0, uplo, &n, &
n, &kd, &kd, &c_n1, &imat, &nfail, &nerrs,
nout);
goto L60;
}
} else if (izero > 0) {
/* Use the same matrix for types 3 and 4 as for type */
/* 2 by copying back the zeroed out column, */
iw = (lda << 1) + 1;
if (iuplo == 1) {
ioff = (izero - 1) * ldab + kd + 1;
i__4 = izero - i1;
ccopy_(&i__4, &work[iw], &c__1, &a[ioff - izero +
i1], &c__1);
iw = iw + izero - i1;
i__4 = i2 - izero + 1;
/* Computing MAX */
i__6 = ldab - 1;
i__5 = max(i__6,1);
ccopy_(&i__4, &work[iw], &c__1, &a[ioff], &i__5);
} else {
ioff = (i1 - 1) * ldab + 1;
i__4 = izero - i1;
/* Computing MAX */
i__6 = ldab - 1;
i__5 = max(i__6,1);
ccopy_(&i__4, &work[iw], &c__1, &a[ioff + izero -
i1], &i__5);
ioff = (izero - 1) * ldab + 1;
iw = iw + izero - i1;
i__4 = i2 - izero + 1;
ccopy_(&i__4, &work[iw], &c__1, &a[ioff], &c__1);
}
}
/* For types 2-4, zero one row and column of the matrix */
/* to test that INFO is returned correctly. */
izero = 0;
if (zerot) {
if (imat == 2) {
izero = 1;
} else if (imat == 3) {
izero = n;
} else {
izero = n / 2 + 1;
}
/* Save the zeroed out row and column in WORK(*,3) */
iw = lda << 1;
/* Computing MIN */
i__5 = (kd << 1) + 1;
i__4 = min(i__5,n);
for (i__ = 1; i__ <= i__4; ++i__) {
i__5 = iw + i__;
work[i__5].r = 0.f, work[i__5].i = 0.f;
/* L20: */
}
++iw;
/* Computing MAX */
i__4 = izero - kd;
i1 = max(i__4,1);
/* Computing MIN */
i__4 = izero + kd;
i2 = min(i__4,n);
if (iuplo == 1) {
ioff = (izero - 1) * ldab + kd + 1;
i__4 = izero - i1;
cswap_(&i__4, &a[ioff - izero + i1], &c__1, &work[
iw], &c__1);
iw = iw + izero - i1;
i__4 = i2 - izero + 1;
/* Computing MAX */
i__6 = ldab - 1;
i__5 = max(i__6,1);
cswap_(&i__4, &a[ioff], &i__5, &work[iw], &c__1);
} else {
ioff = (i1 - 1) * ldab + 1;
i__4 = izero - i1;
/* Computing MAX */
i__6 = ldab - 1;
i__5 = max(i__6,1);
cswap_(&i__4, &a[ioff + izero - i1], &i__5, &work[
iw], &c__1);
ioff = (izero - 1) * ldab + 1;
iw = iw + izero - i1;
i__4 = i2 - izero + 1;
cswap_(&i__4, &a[ioff], &c__1, &work[iw], &c__1);
}
}
/* Set the imaginary part of the diagonals. */
if (iuplo == 1) {
claipd_(&n, &a[kd + 1], &ldab, &c__0);
} else {
claipd_(&n, &a[1], &ldab, &c__0);
}
/* Do for each value of NB in NBVAL */
i__4 = *nnb;
for (inb = 1; inb <= i__4; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
/* Compute the L*L' or U'*U factorization of the band */
/* matrix. */
i__5 = kd + 1;
clacpy_("Full", &i__5, &n, &a[1], &ldab, &afac[1], &
ldab);
s_copy(srnamc_1.srnamt, "CPBTRF", (ftnlen)32, (ftnlen)
6);
cpbtrf_(uplo, &n, &kd, &afac[1], &ldab, &info);
/* Check error code from CPBTRF. */
if (info != izero) {
alaerh_(path, "CPBTRF", &info, &izero, uplo, &n, &
n, &kd, &kd, &nb, &imat, &nfail, &nerrs,
nout);
goto L50;
}
/* Skip the tests if INFO is not 0. */
if (info != 0) {
goto L50;
}
/* + TEST 1 */
/* Reconstruct matrix from factors and compute */
/* residual. */
i__5 = kd + 1;
clacpy_("Full", &i__5, &n, &afac[1], &ldab, &ainv[1],
&ldab);
cpbt01_(uplo, &n, &kd, &a[1], &ldab, &ainv[1], &ldab,
&rwork[1], result);
/* Print the test ratio if it is .GE. THRESH. */
if (result[0] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___40.ciunit = *nout;
s_wsfe(&io___40);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&kd, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&nb, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&c__1, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[0], (ftnlen)sizeof(
real));
e_wsfe();
++nfail;
}
++nrun;
/* Only do other tests if this is the first blocksize. */
if (inb > 1) {
goto L50;
}
/* Form the inverse of A so we can get a good estimate */
/* of RCONDC = 1/(norm(A) * norm(inv(A))). */
claset_("Full", &n, &n, &c_b50, &c_b51, &ainv[1], &
lda);
s_copy(srnamc_1.srnamt, "CPBTRS", (ftnlen)32, (ftnlen)
6);
cpbtrs_(uplo, &n, &kd, &n, &afac[1], &ldab, &ainv[1],
&lda, &info);
/* Compute RCONDC = 1/(norm(A) * norm(inv(A))). */
anorm = clanhb_("1", uplo, &n, &kd, &a[1], &ldab, &
rwork[1]);
ainvnm = clange_("1", &n, &n, &ainv[1], &lda, &rwork[
1]);
if (anorm <= 0.f || ainvnm <= 0.f) {
rcondc = 1.f;
} else {
rcondc = 1.f / anorm / ainvnm;
}
i__5 = *nns;
for (irhs = 1; irhs <= i__5; ++irhs) {
nrhs = nsval[irhs];
/* + TEST 2 */
/* Solve and compute residual for A * X = B. */
s_copy(srnamc_1.srnamt, "CLARHS", (ftnlen)32, (
ftnlen)6);
clarhs_(path, xtype, uplo, " ", &n, &n, &kd, &kd,
&nrhs, &a[1], &ldab, &xact[1], &lda, &b[1]
, &lda, iseed, &info);
clacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &
lda);
s_copy(srnamc_1.srnamt, "CPBTRS", (ftnlen)32, (
ftnlen)6);
cpbtrs_(uplo, &n, &kd, &nrhs, &afac[1], &ldab, &x[
1], &lda, &info);
/* Check error code from CPBTRS. */
if (info != 0) {
alaerh_(path, "CPBTRS", &info, &c__0, uplo, &
n, &n, &kd, &kd, &nrhs, &imat, &nfail,
&nerrs, nout);
}
clacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1],
&lda);
cpbt02_(uplo, &n, &kd, &nrhs, &a[1], &ldab, &x[1],
&lda, &work[1], &lda, &rwork[1], &result[
1]);
/* + TEST 3 */
/* Check solution from generated exact solution. */
cget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[2]);
/* + TESTS 4, 5, and 6 */
/* Use iterative refinement to improve the solution. */
s_copy(srnamc_1.srnamt, "CPBRFS", (ftnlen)32, (
ftnlen)6);
cpbrfs_(uplo, &n, &kd, &nrhs, &a[1], &ldab, &afac[
1], &ldab, &b[1], &lda, &x[1], &lda, &
rwork[1], &rwork[nrhs + 1], &work[1], &
rwork[(nrhs << 1) + 1], &info);
/* Check error code from CPBRFS. */
if (info != 0) {
alaerh_(path, "CPBRFS", &info, &c__0, uplo, &
n, &n, &kd, &kd, &nrhs, &imat, &nfail,
&nerrs, nout);
}
cget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[3]);
cpbt05_(uplo, &n, &kd, &nrhs, &a[1], &ldab, &b[1],
&lda, &x[1], &lda, &xact[1], &lda, &
rwork[1], &rwork[nrhs + 1], &result[4]);
/* Print information about the tests that did not */
/* pass the threshold. */
for (k = 2; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___46.ciunit = *nout;
s_wsfe(&io___46);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&kd, (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(real));
e_wsfe();
++nfail;
}
/* L30: */
}
nrun += 5;
/* L40: */
}
/* + TEST 7 */
/* Get an estimate of RCOND = 1/CNDNUM. */
s_copy(srnamc_1.srnamt, "CPBCON", (ftnlen)32, (ftnlen)
6);
cpbcon_(uplo, &n, &kd, &afac[1], &ldab, &anorm, &
rcond, &work[1], &rwork[1], &info);
/* Check error code from CPBCON. */
if (info != 0) {
alaerh_(path, "CPBCON", &info, &c__0, uplo, &n, &
n, &kd, &kd, &c_n1, &imat, &nfail, &nerrs,
nout);
}
result[6] = sget06_(&rcond, &rcondc);
/* Print the test ratio if it is .GE. THRESH. */
if (result[6] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___48.ciunit = *nout;
s_wsfe(&io___48);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&kd, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&c__7, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[6], (ftnlen)sizeof(
real));
e_wsfe();
++nfail;
}
++nrun;
L50:
;
}
L60:
;
}
/* L70: */
}
/* L80: */
}
/* L90: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of CCHKPB */
} /* cchkpb_ */
/* Subroutine */ int cpbrfs_(char *uplo, integer *n, integer *kd, integer *
nrhs, complex *ab, integer *ldab, complex *afb, integer *ldafb,
complex *b, integer *ldb, complex *x, integer *ldx, real *ferr, real *
berr, complex *work, real *rwork, integer *info)
{
/* -- LAPACK routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CPBRFS improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian positive definite
and banded, 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.
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
AB (input) REAL array, dimension (LDAB,N)
The upper or lower triangle of the Hermitian band matrix A,
stored in the first KD+1 rows of the array. The j-th column
of A is stored in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
AFB (input) COMPLEX array, dimension (LDAFB,N)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H of the band matrix A as computed by
CPBTRF, in the same storage format as A (see AB).
LDAFB (input) INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.
B (input) COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CPBTRS.
On exit, the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j). The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.
BERR (output) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in
any element of A or B that makes X(j) an exact solution).
WORK (workspace) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Internal Parameters
===================
ITMAX is the maximum number of steps of iterative refinement.
=====================================================================
Test the input parameters.
Parameter adjustments
Function Body */
/* Table of constant values */
static complex c_b1 = {1.f,0.f};
static integer c__1 = 1;
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
static integer kase;
static real safe1, safe2;
static integer i, j, k, l;
static real s;
extern /* Subroutine */ int chbmv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
static integer count;
static logical upper;
extern /* Subroutine */ int clacon_(integer *, complex *, complex *, real
*, integer *);
static real xk;
extern doublereal slamch_(char *);
static integer nz;
static real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *), cpbtrs_(
char *, integer *, integer *, integer *, complex *, integer *,
complex *, integer *, integer *);
static real lstres, eps;
#define FERR(I) ferr[(I)-1]
#define BERR(I) berr[(I)-1]
#define WORK(I) work[(I)-1]
#define RWORK(I) rwork[(I)-1]
#define AB(I,J) ab[(I)-1 + ((J)-1)* ( *ldab)]
#define AFB(I,J) afb[(I)-1 + ((J)-1)* ( *ldafb)]
#define B(I,J) b[(I)-1 + ((J)-1)* ( *ldb)]
#define X(I,J) x[(I)-1 + ((J)-1)* ( *ldx)]
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kd < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*ldab < *kd + 1) {
*info = -6;
} else if (*ldafb < *kd + 1) {
*info = -8;
} else if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldx < max(1,*n)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPBRFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= *nrhs; ++j) {
FERR(j) = 0.f;
BERR(j) = 0.f;
/* L10: */
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1
Computing MIN */
i__1 = *n + 1, i__2 = (*kd << 1) + 2;
nz = min(i__1,i__2);
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= *nrhs; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied.
Compute residual R = B - A * X */
ccopy_(n, &B(1,j), &c__1, &WORK(1), &c__1);
q__1.r = -1.f, q__1.i = 0.f;
chbmv_(uplo, n, kd, &q__1, &AB(1,1), ldab, &X(1,j), &
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 matr
ix
or vector Z. If the i-th component of the denominator is le
ss
than SAFE2, then SAFE1 is added to the i-th components of th
e
numerator and denominator before dividing. */
i__2 = *n;
for (i = 1; i <= *n; ++i) {
i__3 = i + j * b_dim1;
RWORK(i) = (r__1 = B(i,j).r, dabs(r__1)) + (r__2 = r_imag(&B(i,j)), dabs(r__2));
/* L30: */
}
/* Compute abs(A)*abs(X) + abs(B). */
if (upper) {
i__2 = *n;
for (k = 1; k <= *n; ++k) {
s = 0.f;
i__3 = k + j * x_dim1;
xk = (r__1 = X(k,j).r, dabs(r__1)) + (r__2 = r_imag(&X(k,j)), dabs(r__2));
l = *kd + 1 - k;
/* Computing MAX */
i__3 = 1, i__4 = k - *kd;
i__5 = k - 1;
for (i = max(1,k-*kd); i <= k-1; ++i) {
i__3 = l + i + k * ab_dim1;
RWORK(i) += ((r__1 = AB(l+i,k).r, dabs(r__1)) + (r__2 =
r_imag(&AB(l+i,k)), dabs(r__2))) *
xk;
i__3 = l + i + k * ab_dim1;
i__4 = i + j * x_dim1;
s += ((r__1 = AB(l+i,k).r, dabs(r__1)) + (r__2 = r_imag(&
AB(l+i,k)), dabs(r__2))) * ((r__3 =
X(i,j).r, dabs(r__3)) + (r__4 = r_imag(&X(i,j)), dabs(r__4)));
/* L40: */
}
i__5 = *kd + 1 + k * ab_dim1;
RWORK(k) = RWORK(k) + (r__1 = AB(*kd+1,k).r, dabs(r__1)) * xk +
s;
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= *n; ++k) {
s = 0.f;
i__5 = k + j * x_dim1;
xk = (r__1 = X(k,j).r, dabs(r__1)) + (r__2 = r_imag(&X(k,j)), dabs(r__2));
i__5 = k * ab_dim1 + 1;
RWORK(k) += (r__1 = AB(1,k).r, dabs(r__1)) * xk;
l = 1 - k;
/* Computing MIN */
i__3 = *n, i__4 = k + *kd;
i__5 = min(i__3,i__4);
for (i = k + 1; i <= min(*n,k+*kd); ++i) {
i__3 = l + i + k * ab_dim1;
RWORK(i) += ((r__1 = AB(l+i,k).r, dabs(r__1)) + (r__2 =
r_imag(&AB(l+i,k)), dabs(r__2))) *
xk;
i__3 = l + i + k * ab_dim1;
i__4 = i + j * x_dim1;
s += ((r__1 = AB(l+i,k).r, dabs(r__1)) + (r__2 = r_imag(&
AB(l+i,k)), dabs(r__2))) * ((r__3 =
X(i,j).r, dabs(r__3)) + (r__4 = r_imag(&X(i,j)), dabs(r__4)));
/* L60: */
}
RWORK(k) += s;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i = 1; i <= *n; ++i) {
if (RWORK(i) > safe2) {
/* Computing MAX */
i__5 = i;
r__3 = s, r__4 = ((r__1 = WORK(i).r, dabs(r__1)) + (r__2 =
r_imag(&WORK(i)), dabs(r__2))) / RWORK(i);
s = dmax(r__3,r__4);
} else {
/* Computing MAX */
i__5 = i;
r__3 = s, r__4 = ((r__1 = WORK(i).r, dabs(r__1)) + (r__2 =
r_imag(&WORK(i)), dabs(r__2)) + safe1) / (RWORK(i) +
safe1);
s = dmax(r__3,r__4);
}
/* L80: */
}
BERR(j) = s;
/* Test stopping criterion. Continue iterating if
1) The residual BERR(J) is larger than machine epsilon, a
nd
2) BERR(J) decreased by at least a factor of 2 during the
last iteration, and
3) At most ITMAX iterations tried. */
if (BERR(j) > eps && BERR(j) * 2.f <= lstres && count <= 5) {
/* Update solution and try again. */
cpbtrs_(uplo, n, kd, &c__1, &AFB(1,1), ldafb, &WORK(1), n,
info);
caxpy_(n, &c_b1, &WORK(1), &c__1, &X(1,j), &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 o
r
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 CLACON 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 <= *n; ++i) {
if (RWORK(i) > safe2) {
i__5 = i;
RWORK(i) = (r__1 = WORK(i).r, dabs(r__1)) + (r__2 = r_imag(
&WORK(i)), dabs(r__2)) + nz * eps * RWORK(i);
} else {
i__5 = i;
RWORK(i) = (r__1 = WORK(i).r, dabs(r__1)) + (r__2 = r_imag(
&WORK(i)), dabs(r__2)) + nz * eps * RWORK(i) + safe1;
}
/* L90: */
}
kase = 0;
L100:
clacon_(n, &WORK(*n + 1), &WORK(1), &FERR(j), &kase);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(A'). */
cpbtrs_(uplo, n, kd, &c__1, &AFB(1,1), ldafb, &WORK(1),
n, info);
i__2 = *n;
for (i = 1; i <= *n; ++i) {
i__5 = i;
i__3 = i;
i__4 = i;
q__1.r = RWORK(i) * WORK(i).r, q__1.i = RWORK(i)
* WORK(i).i;
WORK(i).r = q__1.r, WORK(i).i = q__1.i;
/* L110: */
}
} else if (kase == 2) {
/* Multiply by inv(A)*diag(W). */
i__2 = *n;
for (i = 1; i <= *n; ++i) {
i__5 = i;
i__3 = i;
i__4 = i;
q__1.r = RWORK(i) * WORK(i).r, q__1.i = RWORK(i)
* WORK(i).i;
WORK(i).r = q__1.r, WORK(i).i = q__1.i;
/* L120: */
}
cpbtrs_(uplo, n, kd, &c__1, &AFB(1,1), ldafb, &WORK(1),
n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i = 1; i <= *n; ++i) {
/* Computing MAX */
i__5 = i + j * x_dim1;
r__3 = lstres, r__4 = (r__1 = X(i,j).r, dabs(r__1)) + (r__2 =
r_imag(&X(i,j)), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L130: */
}
if (lstres != 0.f) {
FERR(j) /= lstres;
}
/* L140: */
}
return 0;
/* End of CPBRFS */
} /* cpbrfs_ */
int cpbsvx_(char *fact, char *uplo, int *n, int *kd,
int *nrhs, complex *ab, int *ldab, complex *afb, int *
ldafb, char *equed, float *s, complex *b, int *ldb, complex *x,
int *ldx, float *rcond, float *ferr, float *berr, complex *work,
float *rwork, int *info)
{
/* System generated locals */
int ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
float r__1, r__2;
complex q__1;
/* Local variables */
int i__, j, j1, j2;
float amax, smin, smax;
extern int lsame_(char *, char *);
float scond, anorm;
extern int ccopy_(int *, complex *, int *,
complex *, int *);
int equil, rcequ, upper;
extern double clanhb_(char *, char *, int *, int *, complex *,
int *, float *);
extern int claqhb_(char *, int *, int *, complex
*, int *, float *, float *, float *, char *),
cpbcon_(char *, int *, int *, complex *, int *, float *
, float *, complex *, float *, int *);
extern double slamch_(char *);
int nofact;
extern int clacpy_(char *, int *, int *, complex
*, int *, complex *, int *), xerbla_(char *,
int *), cpbequ_(char *, int *, int *, complex
*, int *, float *, float *, float *, int *), cpbrfs_(
char *, int *, int *, int *, complex *, int *,
complex *, int *, complex *, int *, complex *, int *,
float *, float *, complex *, float *, int *);
float bignum;
extern int cpbtrf_(char *, int *, int *, complex
*, int *, int *);
int infequ;
extern int cpbtrs_(char *, int *, int *, int
*, complex *, int *, complex *, int *, int *);
float smlnum;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CPBSVX 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 band 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', float 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 band matrix, and L is a lower */
/* triangular band 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, AFB contains the factored form of A. */
/* If EQUED = 'Y', the matrix A has been equilibrated */
/* with scaling factors given by S. AB and AFB will not */
/* be modified. */
/* = 'N': The matrix A will be copied to AFB and factored. */
/* = 'E': The matrix A will be equilibrated if necessary, then */
/* copied to AFB 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. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* NRHS (input) INTEGER */
/* The number of right-hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* AB (input/output) COMPLEX array, dimension (LDAB,N) */
/* On entry, the upper or lower triangle of the Hermitian band */
/* matrix A, stored in the first KD+1 rows of the array, except */
/* if FACT = 'F' and EQUED = 'Y', then A must contain the */
/* equilibrated matrix diag(S)*A*diag(S). The j-th column of A */
/* is stored in the j-th column of the array AB as follows: */
/* if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for MAX(1,j-KD)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=MIN(N,j+KD). */
/* See below for further details. */
/* On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by */
/* diag(S)*A*diag(S). */
/* LDAB (input) INTEGER */
/* The leading dimension of the array A. LDAB >= KD+1. */
/* AFB (input or output) COMPLEX array, dimension (LDAFB,N) */
/* If FACT = 'F', then AFB 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 of the band matrix */
/* A, in the same storage format as A (see AB). If EQUED = 'Y', */
/* then AFB is the factored form of the equilibrated matrix A. */
/* If FACT = 'N', then AFB 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. */
/* If FACT = 'E', then AFB 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). */
/* LDAFB (input) INTEGER */
/* The leading dimension of the array AFB. LDAFB >= KD+1. */
/* EQUED (input or output) CHARACTER*1 */
/* Specifies the form of equilibration that was done. */
/* = 'N': No equilibration (always true if FACT = 'N'). */
/* = 'Y': Equilibration was done, i.e., A has been replaced by */
/* diag(S) * A * diag(S). */
/* EQUED is an input argument if FACT = 'F'; otherwise, it is an */
/* output argument. */
/* S (input or output) REAL array, dimension (N) */
/* The scale factors for A; not accessed if EQUED = 'N'. S is */
/* an input argument if FACT = 'F'; otherwise, S is an output */
/* argument. If FACT = 'F' and EQUED = 'Y', each element of S */
/* must be positive. */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS right hand side matrix B. */
/* On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y', */
/* B is overwritten by diag(S) * B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= MAX(1,N). */
/* X (output) COMPLEX array, dimension (LDX,NRHS) */
/* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X to */
/* the original system of equations. Note that if EQUED = 'Y', */
/* A and B are modified on exit, and the solution to the */
/* equilibrated system is inv(diag(S))*X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= MAX(1,N). */
/* RCOND (output) REAL */
/* The estimate of the reciprocal condition number of the matrix */
/* A after equilibration (if done). If RCOND is less than the */
/* machine precision (in particular, if RCOND = 0), the matrix */
/* is singular to working precision. This condition is */
/* indicated by a return code of INFO > 0. */
/* FERR (output) REAL array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) REAL array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) COMPLEX array, dimension (2*N) */
/* RWORK (workspace) REAL array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, and i is */
/* <= N: the leading minor of order i of A is */
/* not positive definite, so the factorization */
/* could not be completed, and the solution has not */
/* been computed. RCOND = 0 is returned. */
/* = N+1: U is nonsingular, but RCOND is less than machine */
/* precision, meaning that the matrix is singular */
/* to working precision. Nevertheless, the */
/* solution and error bounds are computed because */
/* there are a number of situations where the */
/* computed solution can be more accurate than the */
/* value of RCOND would suggest. */
/* Further Details */
/* =============== */
/* The band storage scheme is illustrated by the following example, when */
/* N = 6, KD = 2, and UPLO = 'U': */
/* Two-dimensional storage of the Hermitian matrix A: */
/* a11 a12 a13 */
/* a22 a23 a24 */
/* a33 a34 a35 */
/* a44 a45 a46 */
/* a55 a56 */
/* (aij=conjg(aji)) a66 */
/* Band storage of the upper triangle of A: */
/* * * a13 a24 a35 a46 */
/* * a12 a23 a34 a45 a56 */
/* a11 a22 a33 a44 a55 a66 */
/* Similarly, if UPLO = 'L' the format of A is as follows: */
/* a11 a22 a33 a44 a55 a66 */
/* a21 a32 a43 a54 a65 * */
/* a31 a42 a53 a64 * * */
/* Array elements marked * are not used by the routine. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
afb_dim1 = *ldafb;
afb_offset = 1 + afb_dim1;
afb -= afb_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");
upper = lsame_(uplo, "U");
if (nofact || equil) {
*(unsigned char *)equed = 'N';
rcequ = FALSE;
} else {
rcequ = lsame_(equed, "Y");
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
}
/* Test the input parameters. */
if (! nofact && ! equil && ! lsame_(fact, "F")) {
*info = -1;
} else if (! upper && ! lsame_(uplo, "L")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*kd < 0) {
*info = -4;
} else if (*nrhs < 0) {
*info = -5;
} else if (*ldab < *kd + 1) {
*info = -7;
} else if (*ldafb < *kd + 1) {
*info = -9;
} else if (lsame_(fact, "F") && ! (rcequ || lsame_(
equed, "N"))) {
*info = -10;
} else {
if (rcequ) {
smin = bignum;
smax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = smin, r__2 = s[j];
smin = MIN(r__1,r__2);
/* Computing MAX */
r__1 = smax, r__2 = s[j];
smax = MAX(r__1,r__2);
/* L10: */
}
if (smin <= 0.f) {
*info = -11;
} else if (*n > 0) {
scond = MAX(smin,smlnum) / MIN(smax,bignum);
} else {
scond = 1.f;
}
}
if (*info == 0) {
if (*ldb < MAX(1,*n)) {
*info = -13;
} else if (*ldx < MAX(1,*n)) {
*info = -15;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPBSVX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
cpbequ_(uplo, n, kd, &ab[ab_offset], ldab, &s[1], &scond, &amax, &
infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
claqhb_(uplo, n, kd, &ab[ab_offset], ldab, &s[1], &scond, &amax,
equed);
rcequ = lsame_(equed, "Y");
}
}
/* Scale the right-hand side. */
if (rcequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__;
i__5 = i__ + j * b_dim1;
q__1.r = s[i__4] * b[i__5].r, q__1.i = s[i__4] * b[i__5].i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L20: */
}
/* L30: */
}
}
if (nofact || equil) {
/* Compute the Cholesky factorization A = U'*U or A = L*L'. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = j - *kd;
j1 = MAX(i__2,1);
i__2 = j - j1 + 1;
ccopy_(&i__2, &ab[*kd + 1 - j + j1 + j * ab_dim1], &c__1, &
afb[*kd + 1 - j + j1 + j * afb_dim1], &c__1);
/* L40: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__2 = j + *kd;
j2 = MIN(i__2,*n);
i__2 = j2 - j + 1;
ccopy_(&i__2, &ab[j * ab_dim1 + 1], &c__1, &afb[j * afb_dim1
+ 1], &c__1);
/* L50: */
}
}
cpbtrf_(uplo, n, kd, &afb[afb_offset], ldafb, info);
/* Return if INFO is non-zero. */
if (*info > 0) {
*rcond = 0.f;
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = clanhb_("1", uplo, n, kd, &ab[ab_offset], ldab, &rwork[1]);
/* Compute the reciprocal of the condition number of A. */
cpbcon_(uplo, n, kd, &afb[afb_offset], ldafb, &anorm, rcond, &work[1], &
rwork[1], info);
/* Compute the solution matrix X. */
clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
cpbtrs_(uplo, n, kd, nrhs, &afb[afb_offset], ldafb, &x[x_offset], ldx,
info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
cpbrfs_(uplo, n, kd, nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb,
&b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1]
, &rwork[1], info);
/* Transform the solution matrix X to a solution of the original */
/* system. */
if (rcequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * x_dim1;
i__4 = i__;
i__5 = i__ + j * x_dim1;
q__1.r = s[i__4] * x[i__5].r, q__1.i = s[i__4] * x[i__5].i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
/* L60: */
}
/* L70: */
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] /= scond;
/* L80: */
}
}
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon")) {
*info = *n + 1;
}
return 0;
/* End of CPBSVX */
} /* cpbsvx_ */
/* Subroutine */ int cpbrfs_(char *uplo, integer *n, integer *kd, integer *
nrhs, complex *ab, integer *ldab, complex *afb, integer *ldafb,
complex *b, integer *ldb, complex *x, integer *ldx, real *ferr, real *
berr, complex *work, real *rwork, integer *info, ftnlen uplo_len)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
static integer i__, j, k, l;
static real s, xk;
static integer nz;
static real eps;
static integer kase;
static real safe1, safe2;
extern /* Subroutine */ int chbmv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *, ftnlen);
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
static integer count;
static logical upper;
extern /* Subroutine */ int clacon_(integer *, complex *, complex *, real
*, integer *);
extern doublereal slamch_(char *, ftnlen);
static real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), cpbtrs_(
char *, integer *, integer *, integer *, complex *, integer *,
complex *, integer *, integer *, ftnlen);
static real lstres;
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CPBRFS improves the computed solution to a system of linear */
/* equations when the coefficient matrix is Hermitian positive definite */
/* and banded, 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. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* AB (input) COMPLEX array, dimension (LDAB,N) */
/* The upper or lower triangle of the Hermitian band matrix A, */
/* stored in the first KD+1 rows of the array. The j-th column */
/* of A is stored in the j-th column of the array AB as follows: */
/* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* AFB (input) COMPLEX array, dimension (LDAFB,N) */
/* The triangular factor U or L from the Cholesky factorization */
/* A = U**H*U or A = L*L**H of the band matrix A as computed by */
/* CPBTRF, in the same storage format as A (see AB). */
/* LDAFB (input) INTEGER */
/* The leading dimension of the array AFB. LDAFB >= KD+1. */
/* B (input) COMPLEX array, dimension (LDB,NRHS) */
/* The right hand side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (input/output) COMPLEX array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by CPBTRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* FERR (output) REAL array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) REAL array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) COMPLEX array, dimension (2*N) */
/* RWORK (workspace) REAL array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Internal Parameters */
/* =================== */
/* ITMAX is the maximum number of steps of iterative refinement. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
afb_dim1 = *ldafb;
afb_offset = 1 + afb_dim1;
afb -= afb_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", (ftnlen)1, (ftnlen)1);
if (! upper && ! lsame_(uplo, "L", (ftnlen)1, (ftnlen)1)) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kd < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*ldab < *kd + 1) {
*info = -6;
} else if (*ldafb < *kd + 1) {
*info = -8;
} else if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldx < max(1,*n)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPBRFS", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
/* Computing MIN */
i__1 = *n + 1, i__2 = (*kd << 1) + 2;
nz = min(i__1,i__2);
eps = slamch_("Epsilon", (ftnlen)7);
safmin = slamch_("Safe minimum", (ftnlen)12);
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - A * X */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
q__1.r = -1.f, q__1.i = -0.f;
chbmv_(uplo, n, kd, &q__1, &ab[ab_offset], ldab, &x[j * x_dim1 + 1], &
c__1, &c_b1, &work[1], &c__1, (ftnlen)1);
/* Compute componentwise relative backward error from formula */
/* max(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. If the i-th component of the denominator is less */
/* than SAFE2, then SAFE1 is added to the i-th components of the */
/* numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
rwork[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[
i__ + j * b_dim1]), dabs(r__2));
/* L30: */
}
/* Compute abs(A)*abs(X) + abs(B). */
if (upper) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[k + j
* x_dim1]), dabs(r__2));
l = *kd + 1 - k;
/* Computing MAX */
i__3 = 1, i__4 = k - *kd;
i__5 = k - 1;
for (i__ = max(i__3,i__4); i__ <= i__5; ++i__) {
i__3 = l + i__ + k * ab_dim1;
rwork[i__] += ((r__1 = ab[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&ab[l + i__ + k * ab_dim1]), dabs(r__2))) *
xk;
i__3 = l + i__ + k * ab_dim1;
i__4 = i__ + j * x_dim1;
s += ((r__1 = ab[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
ab[l + i__ + k * ab_dim1]), dabs(r__2))) * ((r__3
= x[i__4].r, dabs(r__3)) + (r__4 = r_imag(&x[i__
+ j * x_dim1]), dabs(r__4)));
/* L40: */
}
i__5 = *kd + 1 + k * ab_dim1;
rwork[k] = rwork[k] + (r__1 = ab[i__5].r, dabs(r__1)) * xk +
s;
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__5 = k + j * x_dim1;
xk = (r__1 = x[i__5].r, dabs(r__1)) + (r__2 = r_imag(&x[k + j
* x_dim1]), dabs(r__2));
i__5 = k * ab_dim1 + 1;
rwork[k] += (r__1 = ab[i__5].r, dabs(r__1)) * xk;
l = 1 - k;
/* Computing MIN */
i__3 = *n, i__4 = k + *kd;
i__5 = min(i__3,i__4);
for (i__ = k + 1; i__ <= i__5; ++i__) {
i__3 = l + i__ + k * ab_dim1;
rwork[i__] += ((r__1 = ab[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&ab[l + i__ + k * ab_dim1]), dabs(r__2))) *
xk;
i__3 = l + i__ + k * ab_dim1;
i__4 = i__ + j * x_dim1;
s += ((r__1 = ab[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
ab[l + i__ + k * ab_dim1]), dabs(r__2))) * ((r__3
= x[i__4].r, dabs(r__3)) + (r__4 = r_imag(&x[i__
+ j * x_dim1]), dabs(r__4)));
/* L60: */
}
rwork[k] += s;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__5 = i__;
r__3 = s, r__4 = ((r__1 = work[i__5].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2))) / rwork[i__];
s = dmax(r__3,r__4);
} else {
/* Computing MAX */
i__5 = i__;
r__3 = s, r__4 = ((r__1 = work[i__5].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + safe1) / (rwork[i__]
+ safe1);
s = dmax(r__3,r__4);
}
/* L80: */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if */
/* 1) The residual BERR(J) is larger than machine epsilon, and */
/* 2) BERR(J) decreased by at least a factor of 2 during the */
/* last iteration, and */
/* 3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
/* Update solution and try again. */
cpbtrs_(uplo, n, kd, &c__1, &afb[afb_offset], ldafb, &work[1], n,
info, (ftnlen)1);
caxpy_(n, &c_b1, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
lstres = berr[j];
++count;
goto L20;
}
/* Bound error from formula */
/* norm(X - XTRUE) / norm(X) .le. FERR = */
/* norm( abs(inv(A))* */
/* ( abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) / norm(X) */
/* where */
/* norm(Z) is the magnitude of the largest component of Z */
/* inv(A) is the inverse of A */
/* abs(Z) is the componentwise absolute value of the matrix or */
/* vector Z */
/* NZ is the maximum number of nonzeros in any row of A, plus 1 */
/* EPS is machine epsilon */
/* The i-th component of abs(R)+NZ*EPS*(abs(A)*abs(X)+abs(B)) */
/* is incremented by SAFE1 if the i-th component of */
/* abs(A)*abs(X) + abs(B) is less than SAFE2. */
/* Use CLACON 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__5 = i__;
rwork[i__] = (r__1 = work[i__5].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__];
} else {
i__5 = i__;
rwork[i__] = (r__1 = work[i__5].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
clacon_(n, &work[*n + 1], &work[1], &ferr[j], &kase);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(A'). */
cpbtrs_(uplo, n, kd, &c__1, &afb[afb_offset], ldafb, &work[1],
n, info, (ftnlen)1);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__5 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = rwork[i__3] * work[i__4].r, q__1.i = rwork[i__3]
* work[i__4].i;
work[i__5].r = q__1.r, work[i__5].i = q__1.i;
/* L110: */
}
} else if (kase == 2) {
/* Multiply by inv(A)*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__5 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = rwork[i__3] * work[i__4].r, q__1.i = rwork[i__3]
* work[i__4].i;
work[i__5].r = q__1.r, work[i__5].i = q__1.i;
/* L120: */
}
cpbtrs_(uplo, n, kd, &c__1, &afb[afb_offset], ldafb, &work[1],
n, info, (ftnlen)1);
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__5 = i__ + j * x_dim1;
r__3 = lstres, r__4 = (r__1 = x[i__5].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L130: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of CPBRFS */
} /* cpbrfs_ */
