/* Subroutine */ int sptsvx_(char *fact, integer *n, integer *nrhs, real *d__,
real *e, real *df, real *ef, real *b, integer *ldb, real *x, integer
*ldx, real *rcond, real *ferr, real *berr, real *work, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
SPTSVX uses the factorization A = L*D*L**T to compute the solution
to a real system of linear equations A*X = B, where A is an N-by-N
symmetric positive definite tridiagonal matrix and X and B are
N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the matrix A is factored as A = L*D*L**T, where L
is a unit lower bidiagonal matrix and D is diagonal. The
factorization can also be regarded as having the form
A = U**T*D*U.
2. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
Arguments
=========
FACT (input) CHARACTER*1
Specifies whether or not the factored form of A has been
supplied on entry.
= 'F': On entry, DF and EF contain the factored form of A.
D, E, DF, and EF will not be modified.
= 'N': The matrix A will be copied to DF and EF and
factored.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
D (input) REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.
E (input) REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A.
DF (input or output) REAL array, dimension (N)
If FACT = 'F', then DF is an input argument and on entry
contains the n diagonal elements of the diagonal matrix D
from the L*D*L**T factorization of A.
If FACT = 'N', then DF is an output argument and on exit
contains the n diagonal elements of the diagonal matrix D
from the L*D*L**T factorization of A.
EF (input or output) REAL array, dimension (N-1)
If FACT = 'F', then EF is an input argument and on entry
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**T factorization of A.
If FACT = 'N', then EF is an output argument and on exit
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**T factorization of A.
B (input) REAL array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (output) REAL array, dimension (LDX,NRHS)
If INFO = 0 of INFO = N+1, the N-by-NRHS solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
RCOND (output) REAL
The reciprocal condition number of the matrix A. If RCOND
is less than the machine precision (in particular, if
RCOND = 0), the matrix is singular to working precision.
This condition is indicated by a return code of INFO > 0.
FERR (output) REAL array, dimension (NRHS)
The forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j).
BERR (output) 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) REAL array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is
<= N: the leading minor of order i of A is
not positive definite, so the factorization
could not be completed, and the solution has not
been computed. RCOND = 0 is returned.
= N+1: U is nonsingular, but RCOND is less than machine
precision, meaning that the matrix is singular
to working precision. Nevertheless, the
solution and error bounds are computed because
there are a number of situations where the
computed solution can be more accurate than the
value of RCOND would suggest.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
static real anorm;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *);
extern doublereal slamch_(char *);
static logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *), slacpy_(
char *, integer *, integer *, real *, integer *, real *, integer *
);
extern doublereal slanst_(char *, integer *, real *, real *);
extern /* Subroutine */ int sptcon_(integer *, real *, real *, real *,
real *, real *, integer *), sptrfs_(integer *, integer *, real *,
real *, real *, real *, real *, integer *, real *, integer *,
real *, real *, real *, integer *), spttrf_(integer *, real *,
real *, integer *), spttrs_(integer *, integer *, real *, real *,
real *, integer *, integer *);
--d__;
--e;
--df;
--ef;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
--ferr;
--berr;
--work;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
if (! nofact && ! lsame_(fact, "F")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < max(1,*n)) {
*info = -9;
} else if (*ldx < max(1,*n)) {
*info = -11;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SPTSVX", &i__1);
return 0;
}
if (nofact) {
/* Compute the L*D*L' (or U'*D*U) factorization of A. */
scopy_(n, &d__[1], &c__1, &df[1], &c__1);
if (*n > 1) {
i__1 = *n - 1;
scopy_(&i__1, &e[1], &c__1, &ef[1], &c__1);
}
spttrf_(n, &df[1], &ef[1], info);
/* Return if INFO is non-zero. */
if (*info != 0) {
if (*info > 0) {
*rcond = 0.f;
}
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = slanst_("1", n, &d__[1], &e[1]);
/* Compute the reciprocal of the condition number of A. */
sptcon_(n, &df[1], &ef[1], &anorm, rcond, &work[1], info);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon")) {
*info = *n + 1;
}
/* Compute the solution vectors X. */
slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
spttrs_(n, nrhs, &df[1], &ef[1], &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solutions and
compute error bounds and backward error estimates for them. */
sptrfs_(n, nrhs, &d__[1], &e[1], &df[1], &ef[1], &b[b_offset], ldb, &x[
x_offset], ldx, &ferr[1], &berr[1], &work[1], info);
return 0;
/* End of SPTSVX */
} /* sptsvx_ */
/* Subroutine */ int serrgt_(char *path, integer *nunit)
{
/* System generated locals */
real r__1;
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
real b[2], c__[2], d__[2], e[2], f[2], w[2], x[2];
char c2[2];
real r1[2], r2[2], cf[2], df[2], ef[2];
integer ip[2], iw[2], info;
real rcond, anorm;
extern /* Subroutine */ int alaesm_(char *, logical *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), sgtcon_(char *, integer *, real *, real *,
real *, real *, integer *, real *, real *, real *, integer *,
integer *), sptcon_(integer *, real *, real *, real *,
real *, real *, integer *), sgtrfs_(char *, integer *, integer *,
real *, real *, real *, real *, real *, real *, real *, integer *,
real *, integer *, real *, integer *, real *, real *, real *,
integer *, integer *), sgttrf_(integer *, real *, real *,
real *, real *, integer *, integer *), sptrfs_(integer *, integer
*, real *, real *, real *, real *, real *, integer *, real *,
integer *, real *, real *, real *, integer *), spttrf_(integer *,
real *, real *, integer *), sgttrs_(char *, integer *, integer *,
real *, real *, real *, real *, integer *, real *, integer *,
integer *), spttrs_(integer *, integer *, real *, real *,
real *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SERRGT tests the error exits for the REAL tridiagonal */
/* routines. */
/* 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 .. */
/* .. */
/* .. 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);
d__[0] = 1.f;
d__[1] = 2.f;
df[0] = 1.f;
df[1] = 2.f;
e[0] = 3.f;
e[1] = 4.f;
ef[0] = 3.f;
ef[1] = 4.f;
anorm = 1.f;
infoc_1.ok = TRUE_;
if (lsamen_(&c__2, c2, "GT")) {
/* Test error exits for the general tridiagonal routines. */
/* SGTTRF */
s_copy(srnamc_1.srnamt, "SGTTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgttrf_(&c_n1, c__, d__, e, f, ip, &info);
chkxer_("SGTTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGTTRS */
s_copy(srnamc_1.srnamt, "SGTTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgttrs_("/", &c__0, &c__0, c__, d__, e, f, ip, x, &c__1, &info);
chkxer_("SGTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgttrs_("N", &c_n1, &c__0, c__, d__, e, f, ip, x, &c__1, &info);
chkxer_("SGTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgttrs_("N", &c__0, &c_n1, c__, d__, e, f, ip, x, &c__1, &info);
chkxer_("SGTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgttrs_("N", &c__2, &c__1, c__, d__, e, f, ip, x, &c__1, &info);
chkxer_("SGTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGTRFS */
s_copy(srnamc_1.srnamt, "SGTRFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgtrfs_("/", &c__0, &c__0, c__, d__, e, cf, df, ef, f, ip, b, &c__1,
x, &c__1, r1, r2, w, iw, &info);
chkxer_("SGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgtrfs_("N", &c_n1, &c__0, c__, d__, e, cf, df, ef, f, ip, b, &c__1,
x, &c__1, r1, r2, w, iw, &info);
chkxer_("SGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgtrfs_("N", &c__0, &c_n1, c__, d__, e, cf, df, ef, f, ip, b, &c__1,
x, &c__1, r1, r2, w, iw, &info);
chkxer_("SGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
sgtrfs_("N", &c__2, &c__1, c__, d__, e, cf, df, ef, f, ip, b, &c__1,
x, &c__2, r1, r2, w, iw, &info);
chkxer_("SGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 15;
sgtrfs_("N", &c__2, &c__1, c__, d__, e, cf, df, ef, f, ip, b, &c__2,
x, &c__1, r1, r2, w, iw, &info);
chkxer_("SGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGTCON */
s_copy(srnamc_1.srnamt, "SGTCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgtcon_("/", &c__0, c__, d__, e, f, ip, &anorm, &rcond, w, iw, &info);
chkxer_("SGTCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgtcon_("I", &c_n1, c__, d__, e, f, ip, &anorm, &rcond, w, iw, &info);
chkxer_("SGTCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
r__1 = -anorm;
sgtcon_("I", &c__0, c__, d__, e, f, ip, &r__1, &rcond, w, iw, &info);
chkxer_("SGTCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
} else if (lsamen_(&c__2, c2, "PT")) {
/* Test error exits for the positive definite tridiagonal */
/* routines. */
/* SPTTRF */
s_copy(srnamc_1.srnamt, "SPTTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spttrf_(&c_n1, d__, e, &info);
chkxer_("SPTTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPTTRS */
s_copy(srnamc_1.srnamt, "SPTTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spttrs_(&c_n1, &c__0, d__, e, x, &c__1, &info);
chkxer_("SPTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spttrs_(&c__0, &c_n1, d__, e, x, &c__1, &info);
chkxer_("SPTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
spttrs_(&c__2, &c__1, d__, e, x, &c__1, &info);
chkxer_("SPTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPTRFS */
s_copy(srnamc_1.srnamt, "SPTRFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sptrfs_(&c_n1, &c__0, d__, e, df, ef, b, &c__1, x, &c__1, r1, r2, w, &
info);
chkxer_("SPTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sptrfs_(&c__0, &c_n1, d__, e, df, ef, b, &c__1, x, &c__1, r1, r2, w, &
info);
chkxer_("SPTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sptrfs_(&c__2, &c__1, d__, e, df, ef, b, &c__1, x, &c__2, r1, r2, w, &
info);
chkxer_("SPTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sptrfs_(&c__2, &c__1, d__, e, df, ef, b, &c__2, x, &c__1, r1, r2, w, &
info);
chkxer_("SPTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPTCON */
s_copy(srnamc_1.srnamt, "SPTCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sptcon_(&c_n1, d__, e, &anorm, &rcond, w, &info);
chkxer_("SPTCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
r__1 = -anorm;
sptcon_(&c__0, d__, e, &r__1, &rcond, w, &info);
chkxer_("SPTCON", &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 SERRGT */
} /* serrgt_ */
/* Subroutine */
int sptsvx_(char *fact, integer *n, integer *nrhs, real *d__, real *e, real *df, real *ef, real *b, integer *ldb, real *x, integer *ldx, real *rcond, real *ferr, real *berr, real *work, integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
real anorm;
extern /* Subroutine */
int scopy_(integer *, real *, integer *, real *, integer *);
extern real slamch_(char *);
logical nofact;
extern /* Subroutine */
int xerbla_(char *, integer *), slacpy_( char *, integer *, integer *, real *, integer *, real *, integer * );
extern real slanst_(char *, integer *, real *, real *);
extern /* Subroutine */
int sptcon_(integer *, real *, real *, real *, real *, real *, integer *), sptrfs_(integer *, integer *, real *, real *, real *, real *, real *, integer *, real *, integer *, real *, real *, real *, integer *), spttrf_(integer *, real *, real *, integer *), spttrs_(integer *, integer *, real *, real *, real *, integer *, integer *);
/* -- LAPACK driver routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
--e;
--df;
--ef;
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;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
if (! nofact && ! lsame_(fact, "F"))
{
*info = -1;
}
else if (*n < 0)
{
*info = -2;
}
else if (*nrhs < 0)
{
*info = -3;
}
else if (*ldb < max(1,*n))
{
*info = -9;
}
else if (*ldx < max(1,*n))
{
*info = -11;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("SPTSVX", &i__1);
return 0;
}
if (nofact)
{
/* Compute the L*D*L**T (or U**T*D*U) factorization of A. */
scopy_(n, &d__[1], &c__1, &df[1], &c__1);
if (*n > 1)
{
i__1 = *n - 1;
scopy_(&i__1, &e[1], &c__1, &ef[1], &c__1);
}
spttrf_(n, &df[1], &ef[1], info);
/* Return if INFO is non-zero. */
if (*info > 0)
{
*rcond = 0.f;
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = slanst_("1", n, &d__[1], &e[1]);
/* Compute the reciprocal of the condition number of A. */
sptcon_(n, &df[1], &ef[1], &anorm, rcond, &work[1], info);
/* Compute the solution vectors X. */
slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
spttrs_(n, nrhs, &df[1], &ef[1], &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solutions and */
/* compute error bounds and backward error estimates for them. */
sptrfs_(n, nrhs, &d__[1], &e[1], &df[1], &ef[1], &b[b_offset], ldb, &x[ x_offset], ldx, &ferr[1], &berr[1], &work[1], info);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon"))
{
*info = *n + 1;
}
return 0;
/* End of SPTSVX */
}
