/* Subroutine */ int dspsvx_(char *fact, char *uplo, integer *n, integer *
nrhs, doublereal *ap, doublereal *afp, integer *ipiv, doublereal *b,
integer *ldb, doublereal *x, integer *ldx, doublereal *rcond,
doublereal *ferr, doublereal *berr, doublereal *work, integer *iwork,
integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
doublereal anorm;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
extern doublereal dlamch_(char *);
logical nofact;
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
xerbla_(char *, integer *);
extern doublereal dlansp_(char *, char *, integer *, doublereal *,
doublereal *);
extern /* Subroutine */ int dspcon_(char *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, integer *,
integer *), dsprfs_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *, integer *), dsptrf_(char *, integer *,
doublereal *, integer *, integer *), dsptrs_(char *,
integer *, integer *, doublereal *, integer *, doublereal *,
integer *, integer *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DSPSVX uses the diagonal pivoting factorization A = U*D*U**T or */
/* 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 matrix stored */
/* in packed format and X and B are N-by-NRHS matrices. */
/* Error bounds on the solution and a condition estimate are also */
/* provided. */
/* Description */
/* =========== */
/* The following steps are performed: */
/* 1. If FACT = 'N', the diagonal pivoting method is used to factor A as */
/* A = U * D * U**T, if UPLO = 'U', or */
/* A = L * D * L**T, if UPLO = 'L', */
/* where U (or L) is a product of permutation and unit upper (lower) */
/* triangular matrices and D is symmetric and block diagonal with */
/* 1-by-1 and 2-by-2 diagonal blocks. */
/* 2. If some D(i,i)=0, so that D is exactly singular, 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, AFP and IPIV contain the factored form of */
/* A. AP, AFP and IPIV will not be modified. */
/* = 'N': The matrix A will be copied to AFP and factored. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* The upper or lower triangle of the symmetric matrix A, packed */
/* columnwise in a linear array. The j-th column of A is stored */
/* in the array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */
/* See below for further details. */
/* AFP (input or output) DOUBLE PRECISION array, dimension */
/* (N*(N+1)/2) */
/* If FACT = 'F', then AFP is an input argument and on entry */
/* contains the block diagonal matrix D and the multipliers used */
/* to obtain the factor U or L from the factorization */
/* A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as */
/* a packed triangular matrix in the same storage format as A. */
/* If FACT = 'N', then AFP is an output argument and on exit */
/* contains the block diagonal matrix D and the multipliers used */
/* to obtain the factor U or L from the factorization */
/* A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as */
/* a packed triangular matrix in the same storage format as A. */
/* IPIV (input or output) INTEGER array, dimension (N) */
/* If FACT = 'F', then IPIV is an input argument and on entry */
/* contains details of the interchanges and the block structure */
/* of D, as determined by DSPTRF. */
/* If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
/* interchanged and D(k,k) is a 1-by-1 diagonal block. */
/* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */
/* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */
/* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = */
/* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */
/* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */
/* If FACT = 'N', then IPIV is an output argument and on exit */
/* contains details of the interchanges and the block structure */
/* of D, as determined by DSPTRF. */
/* B (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS) */
/* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* RCOND (output) DOUBLE PRECISION */
/* The estimate of the reciprocal condition number of the matrix */
/* A. If RCOND is less than the machine precision (in */
/* particular, if RCOND = 0), the matrix is singular to working */
/* precision. This condition is indicated by a return code of */
/* INFO > 0. */
/* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (3*N) */
/* IWORK (workspace) INTEGER 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: D(i,i) is exactly zero. The factorization */
/* has been completed but the factor D is exactly */
/* singular, so the solution and error bounds could */
/* not be computed. RCOND = 0 is returned. */
/* = N+1: D is nonsingular, but RCOND is less than machine */
/* precision, meaning that the matrix is singular */
/* to working precision. Nevertheless, the */
/* solution and error bounds are computed because */
/* there are a number of situations where the */
/* computed solution can be more accurate than the */
/* value of RCOND would suggest. */
/* Further Details */
/* =============== */
/* The packed storage scheme is illustrated by the following example */
/* when N = 4, UPLO = 'U': */
/* Two-dimensional storage of the symmetric matrix A: */
/* a11 a12 a13 a14 */
/* a22 a23 a24 */
/* a33 a34 (aij = aji) */
/* a44 */
/* Packed storage of the upper triangle of A: */
/* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
--afp;
--ipiv;
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;
--iwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
if (! nofact && ! lsame_(fact, "F")) {
*info = -1;
} else if (! lsame_(uplo, "U") && ! lsame_(uplo,
"L")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*ldb < max(1,*n)) {
*info = -9;
} else if (*ldx < max(1,*n)) {
*info = -11;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSPSVX", &i__1);
return 0;
}
if (nofact) {
/* Compute the factorization A = U*D*U' or A = L*D*L'. */
i__1 = *n * (*n + 1) / 2;
dcopy_(&i__1, &ap[1], &c__1, &afp[1], &c__1);
dsptrf_(uplo, n, &afp[1], &ipiv[1], info);
/* Return if INFO is non-zero. */
if (*info > 0) {
*rcond = 0.;
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = dlansp_("I", uplo, n, &ap[1], &work[1]);
/* Compute the reciprocal of the condition number of A. */
dspcon_(uplo, n, &afp[1], &ipiv[1], &anorm, rcond, &work[1], &iwork[1],
info);
/* Compute the solution vectors X. */
dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
dsptrs_(uplo, n, nrhs, &afp[1], &ipiv[1], &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solutions and */
/* compute error bounds and backward error estimates for them. */
dsprfs_(uplo, n, nrhs, &ap[1], &afp[1], &ipiv[1], &b[b_offset], ldb, &x[
x_offset], ldx, &ferr[1], &berr[1], &work[1], &iwork[1], info);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < dlamch_("Epsilon")) {
*info = *n + 1;
}
return 0;
/* End of DSPSVX */
} /* dspsvx_ */
/* Subroutine */ int dspsv_(char *uplo, integer *n, integer *nrhs, doublereal
*ap, integer *ipiv, doublereal *b, integer *ldb, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
DSPSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix stored in packed format and X
and B are N-by-NRHS matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is symmetric and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.
On exit, the block diagonal matrix D and the multipliers used
to obtain the factor U or L from the factorization
A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as
a packed triangular matrix in the same storage format as A.
IPIV (output) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as
determined by DSPTRF. If IPIV(k) > 0, then rows and columns
k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
then rows and columns k-1 and -IPIV(k) were interchanged and
D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
-IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
diagonal block.
B (input/output) DOUBLE PRECISION 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, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be
computed.
Further Details
===============
The packed storage scheme is illustrated by the following example
when N = 4, UPLO = 'U':
Two-dimensional storage of the symmetric matrix A:
a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = aji)
a44
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
=====================================================================
Test the input parameters.
Parameter adjustments */
/* System generated locals */
integer b_dim1, b_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *), dsptrf_(
char *, integer *, doublereal *, integer *, integer *),
dsptrs_(char *, integer *, integer *, doublereal *, integer *,
doublereal *, integer *, integer *);
--ap;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
*info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSPSV ", &i__1);
return 0;
}
/* Compute the factorization A = U*D*U' or A = L*D*L'. */
dsptrf_(uplo, n, &ap[1], &ipiv[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
dsptrs_(uplo, n, nrhs, &ap[1], &ipiv[1], &b[b_offset], ldb, info);
}
return 0;
/* End of DSPSV */
} /* dspsv_ */
/* Subroutine */ int derrsy_(char *path, integer *nunit)
{
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
static integer info;
static doublereal anrm, a[16] /* was [4][4] */, b[4];
static integer i__, j;
static doublereal w[12], x[4], rcond;
static char c2[2];
static doublereal r1[4], r2[4], af[16] /* was [4][4] */;
extern /* Subroutine */ int dsytf2_(char *, integer *, doublereal *,
integer *, integer *, integer *);
static integer ip[4], iw[4];
extern /* Subroutine */ int alaesm_(char *, logical *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), dspcon_(char *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, integer *,
integer *), dsycon_(char *, integer *, doublereal *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
integer *, integer *), dsprfs_(char *, integer *, integer
*, doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *
, integer *, integer *), dsptrf_(char *, integer *,
doublereal *, integer *, integer *), dsptri_(char *,
integer *, doublereal *, integer *, doublereal *, integer *), dsyrfs_(char *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *, integer *), dsytrf_(char *,
integer *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *), dsytri_(char *, integer *,
doublereal *, integer *, integer *, doublereal *, integer *), dsptrs_(char *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *), dsytrs_(
char *, integer *, integer *, doublereal *, integer *, integer *,
doublereal *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
#define a_ref(a_1,a_2) a[(a_2)*4 + a_1 - 5]
#define af_ref(a_1,a_2) af[(a_2)*4 + a_1 - 5]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
DERRSY tests the error exits for the DOUBLE PRECISION routines
for symmetric indefinite matrices.
Arguments
=========
PATH (input) CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT (input) INTEGER
The unit number for output.
===================================================================== */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Set the variables to innocuous values. */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
a_ref(i__, j) = 1. / (doublereal) (i__ + j);
af_ref(i__, j) = 1. / (doublereal) (i__ + j);
/* L10: */
}
b[j - 1] = 0.;
r1[j - 1] = 0.;
r2[j - 1] = 0.;
w[j - 1] = 0.;
x[j - 1] = 0.;
ip[j - 1] = j;
iw[j - 1] = j;
/* L20: */
}
anrm = 1.;
rcond = 1.;
infoc_1.ok = TRUE_;
if (lsamen_(&c__2, c2, "SY")) {
/* Test error exits of the routines that use the Bunch-Kaufman
factorization of a symmetric indefinite matrix.
DSYTRF */
s_copy(srnamc_1.srnamt, "DSYTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dsytrf_("/", &c__0, a, &c__1, ip, w, &c__1, &info);
chkxer_("DSYTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dsytrf_("U", &c_n1, a, &c__1, ip, w, &c__1, &info);
chkxer_("DSYTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dsytrf_("U", &c__2, a, &c__1, ip, w, &c__4, &info);
chkxer_("DSYTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DSYTF2 */
s_copy(srnamc_1.srnamt, "DSYTF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dsytf2_("/", &c__0, a, &c__1, ip, &info);
chkxer_("DSYTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dsytf2_("U", &c_n1, a, &c__1, ip, &info);
chkxer_("DSYTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dsytf2_("U", &c__2, a, &c__1, ip, &info);
chkxer_("DSYTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DSYTRI */
s_copy(srnamc_1.srnamt, "DSYTRI", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dsytri_("/", &c__0, a, &c__1, ip, w, &info);
chkxer_("DSYTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dsytri_("U", &c_n1, a, &c__1, ip, w, &info);
chkxer_("DSYTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dsytri_("U", &c__2, a, &c__1, ip, w, &info);
chkxer_("DSYTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DSYTRS */
s_copy(srnamc_1.srnamt, "DSYTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dsytrs_("/", &c__0, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("DSYTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dsytrs_("U", &c_n1, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("DSYTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dsytrs_("U", &c__0, &c_n1, a, &c__1, ip, b, &c__1, &info);
chkxer_("DSYTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dsytrs_("U", &c__2, &c__1, a, &c__1, ip, b, &c__2, &info);
chkxer_("DSYTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dsytrs_("U", &c__2, &c__1, a, &c__2, ip, b, &c__1, &info);
chkxer_("DSYTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DSYRFS */
s_copy(srnamc_1.srnamt, "DSYRFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dsyrfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dsyrfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dsyrfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dsyrfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, ip, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dsyrfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, ip, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dsyrfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__1, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
dsyrfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__2, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("DSYRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DSYCON */
s_copy(srnamc_1.srnamt, "DSYCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dsycon_("/", &c__0, a, &c__1, ip, &anrm, &rcond, w, iw, &info);
chkxer_("DSYCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dsycon_("U", &c_n1, a, &c__1, ip, &anrm, &rcond, w, iw, &info);
chkxer_("DSYCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dsycon_("U", &c__2, a, &c__1, ip, &anrm, &rcond, w, iw, &info);
chkxer_("DSYCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
dsycon_("U", &c__1, a, &c__1, ip, &c_b152, &rcond, w, iw, &info);
chkxer_("DSYCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
} else if (lsamen_(&c__2, c2, "SP")) {
/* Test error exits of the routines that use the Bunch-Kaufman
factorization of a symmetric indefinite packed matrix.
DSPTRF */
s_copy(srnamc_1.srnamt, "DSPTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dsptrf_("/", &c__0, a, ip, &info);
chkxer_("DSPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dsptrf_("U", &c_n1, a, ip, &info);
chkxer_("DSPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DSPTRI */
s_copy(srnamc_1.srnamt, "DSPTRI", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dsptri_("/", &c__0, a, ip, w, &info);
chkxer_("DSPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dsptri_("U", &c_n1, a, ip, w, &info);
chkxer_("DSPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DSPTRS */
s_copy(srnamc_1.srnamt, "DSPTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dsptrs_("/", &c__0, &c__0, a, ip, b, &c__1, &info);
chkxer_("DSPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dsptrs_("U", &c_n1, &c__0, a, ip, b, &c__1, &info);
chkxer_("DSPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dsptrs_("U", &c__0, &c_n1, a, ip, b, &c__1, &info);
chkxer_("DSPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dsptrs_("U", &c__2, &c__1, a, ip, b, &c__1, &info);
chkxer_("DSPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DSPRFS */
s_copy(srnamc_1.srnamt, "DSPRFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dsprfs_("/", &c__0, &c__0, a, af, ip, b, &c__1, x, &c__1, r1, r2, w,
iw, &info);
chkxer_("DSPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dsprfs_("U", &c_n1, &c__0, a, af, ip, b, &c__1, x, &c__1, r1, r2, w,
iw, &info);
chkxer_("DSPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dsprfs_("U", &c__0, &c_n1, a, af, ip, b, &c__1, x, &c__1, r1, r2, w,
iw, &info);
chkxer_("DSPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dsprfs_("U", &c__2, &c__1, a, af, ip, b, &c__1, x, &c__2, r1, r2, w,
iw, &info);
chkxer_("DSPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dsprfs_("U", &c__2, &c__1, a, af, ip, b, &c__2, x, &c__1, r1, r2, w,
iw, &info);
chkxer_("DSPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DSPCON */
s_copy(srnamc_1.srnamt, "DSPCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dspcon_("/", &c__0, a, ip, &anrm, &rcond, w, iw, &info);
chkxer_("DSPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dspcon_("U", &c_n1, a, ip, &anrm, &rcond, w, iw, &info);
chkxer_("DSPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dspcon_("U", &c__1, a, ip, &c_b152, &rcond, w, iw, &info);
chkxer_("DSPCON", &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 DERRSY */
} /* derrsy_ */
int dspsv_(char *uplo, int *n, int *nrhs, double
*ap, int *ipiv, double *b, int *ldb, int *info)
{
/* System generated locals */
int b_dim1, b_offset, i__1;
/* Local variables */
extern int lsame_(char *, char *);
extern int xerbla_(char *, int *), dsptrf_(
char *, int *, double *, int *, int *),
dsptrs_(char *, int *, int *, double *, int *,
double *, int *, int *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DSPSV computes the solution to a float system of linear equations */
/* A * X = B, */
/* where A is an N-by-N symmetric matrix stored in packed format and X */
/* and B are N-by-NRHS matrices. */
/* The diagonal pivoting method is used to factor A as */
/* A = U * D * U**T, if UPLO = 'U', or */
/* A = L * D * L**T, if UPLO = 'L', */
/* where U (or L) is a product of permutation and unit upper (lower) */
/* triangular matrices, D is symmetric and block diagonal with 1-by-1 */
/* and 2-by-2 diagonal blocks. The factored form of A is then used to */
/* solve the system of equations A * X = B. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrix B. NRHS >= 0. */
/* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangle of the symmetric matrix */
/* A, packed columnwise in a linear array. The j-th column of A */
/* is stored in the array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* See below for further details. */
/* On exit, the block diagonal matrix D and the multipliers used */
/* to obtain the factor U or L from the factorization */
/* A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as */
/* a packed triangular matrix in the same storage format as A. */
/* IPIV (output) INTEGER array, dimension (N) */
/* Details of the interchanges and the block structure of D, as */
/* determined by DSPTRF. If IPIV(k) > 0, then rows and columns */
/* k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 */
/* diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, */
/* then rows and columns k-1 and -IPIV(k) were interchanged and */
/* D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and */
/* IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and */
/* -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 */
/* diagonal block. */
/* B (input/output) DOUBLE PRECISION 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, D(i,i) is exactly zero. The factorization */
/* has been completed, but the block diagonal matrix D is */
/* exactly singular, so the solution could not be */
/* computed. */
/* Further Details */
/* =============== */
/* The packed storage scheme is illustrated by the following example */
/* when N = 4, UPLO = 'U': */
/* Two-dimensional storage of the symmetric matrix A: */
/* a11 a12 a13 a14 */
/* a22 a23 a24 */
/* a33 a34 (aij = aji) */
/* a44 */
/* Packed storage of the upper triangle of A: */
/* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] */
/* ===================================================================== */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < MAX(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSPSV ", &i__1);
return 0;
}
/* Compute the factorization A = U*D*U' or A = L*D*L'. */
dsptrf_(uplo, n, &ap[1], &ipiv[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
dsptrs_(uplo, n, nrhs, &ap[1], &ipiv[1], &b[b_offset], ldb, info);
}
return 0;
/* End of DSPSV */
} /* dspsv_ */
/* Subroutine */ int dspcon_(char *uplo, integer *n, doublereal *ap, integer *
ipiv, doublereal *anorm, doublereal *rcond, doublereal *work, integer
*iwork, integer *info)
{
/* System generated locals */
integer i__1;
/* Local variables */
integer i__, ip, kase;
extern logical lsame_(char *, char *);
integer isave[3];
logical upper;
extern /* Subroutine */ int dlacn2_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *), xerbla_(char *,
integer *);
doublereal ainvnm;
extern /* Subroutine */ int dsptrs_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *);
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DSPCON estimates the reciprocal of the condition number (in the */
/* 1-norm) of a real symmetric packed matrix A using the factorization */
/* A = U*D*U**T or A = L*D*L**T computed by DSPTRF. */
/* An estimate is obtained for norm(inv(A)), and the reciprocal of the */
/* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the details of the factorization are stored */
/* as an upper or lower triangular matrix. */
/* = 'U': Upper triangular, form is A = U*D*U**T; */
/* = 'L': Lower triangular, form is A = L*D*L**T. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* The block diagonal matrix D and the multipliers used to */
/* obtain the factor U or L as computed by DSPTRF, stored as a */
/* packed triangular matrix. */
/* IPIV (input) INTEGER array, dimension (N) */
/* Details of the interchanges and the block structure of D */
/* as determined by DSPTRF. */
/* ANORM (input) DOUBLE PRECISION */
/* The 1-norm of the original matrix A. */
/* RCOND (output) DOUBLE PRECISION */
/* The reciprocal of the condition number of the matrix A, */
/* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an */
/* estimate of the 1-norm of inv(A) computed in this routine. */
/* WORK (workspace) DOUBLE PRECISION array, dimension (2*N) */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--iwork;
--work;
--ipiv;
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*anorm < 0.) {
*info = -5;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSPCON", &i__1);
return 0;
}
/* Quick return if possible */
*rcond = 0.;
if (*n == 0) {
*rcond = 1.;
return 0;
} else if (*anorm <= 0.) {
return 0;
}
/* Check that the diagonal matrix D is nonsingular. */
if (upper) {
/* Upper triangular storage: examine D from bottom to top */
ip = *n * (*n + 1) / 2;
for (i__ = *n; i__ >= 1; --i__) {
if (ipiv[i__] > 0 && ap[ip] == 0.) {
return 0;
}
ip -= i__;
/* L10: */
}
} else {
/* Lower triangular storage: examine D from top to bottom. */
ip = 1;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (ipiv[i__] > 0 && ap[ip] == 0.) {
return 0;
}
ip = ip + *n - i__ + 1;
/* L20: */
}
}
/* Estimate the 1-norm of the inverse. */
kase = 0;
L30:
dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
if (kase != 0) {
/* Multiply by inv(L*D*L') or inv(U*D*U'). */
dsptrs_(uplo, n, &c__1, &ap[1], &ipiv[1], &work[1], n, info);
goto L30;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.) {
*rcond = 1. / ainvnm / *anorm;
}
return 0;
/* End of DSPCON */
} /* dspcon_ */
/* Subroutine */ int dsprfs_(char *uplo, integer *n, integer *nrhs,
doublereal *ap, doublereal *afp, integer *ipiv, doublereal *b,
integer *ldb, doublereal *x, integer *ldx, doublereal *ferr,
doublereal *berr, doublereal *work, integer *iwork, integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3;
doublereal d__1, d__2, d__3;
/* Local variables */
integer i__, j, k;
doublereal s;
integer ik, kk;
doublereal xk;
integer nz;
doublereal eps;
integer kase;
doublereal safe1, safe2;
integer isave[3];
integer count;
logical upper;
doublereal safmin;
doublereal lstres;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. */
/* Purpose */
/* ======= */
/* DSPRFS improves the computed solution to a system of linear */
/* equations when the coefficient matrix is symmetric indefinite */
/* and packed, and provides error bounds and backward error estimates */
/* for the solution. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* The upper or lower triangle of the symmetric matrix A, packed */
/* columnwise in a linear array. The j-th column of A is stored */
/* in the array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */
/* AFP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* The factored form of the matrix A. AFP contains the block */
/* diagonal matrix D and the multipliers used to obtain the */
/* factor U or L from the factorization A = U*D*U**T or */
/* A = L*D*L**T as computed by DSPTRF, stored as a packed */
/* triangular matrix. */
/* IPIV (input) INTEGER array, dimension (N) */
/* Details of the interchanges and the block structure of D */
/* as determined by DSPTRF. */
/* B (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by DSPTRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (3*N) */
/* IWORK (workspace) INTEGER 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 */
--ap;
--afp;
--ipiv;
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;
--iwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < max(1,*n)) {
*info = -8;
} else if (*ldx < max(1,*n)) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSPRFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.;
berr[j] = 0.;
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = dlamch_("Epsilon");
safmin = dlamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.;
L20:
/* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - A * X */
dcopy_(n, &b[j * b_dim1 + 1], &c__1, &work[*n + 1], &c__1);
dspmv_(uplo, n, &c_b12, &ap[1], &x[j * x_dim1 + 1], &c__1, &c_b14, &
work[*n + 1], &c__1);
/* Compute componentwise relative backward error from formula */
/* max(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. If the i-th component of the denominator is less */
/* than SAFE2, then SAFE1 is added to the i-th components of the */
/* numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[i__] = (d__1 = b[i__ + j * b_dim1], abs(d__1));
}
/* Compute abs(A)*abs(X) + abs(B). */
kk = 1;
if (upper) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.;
xk = (d__1 = x[k + j * x_dim1], abs(d__1));
ik = kk;
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
work[i__] += (d__1 = ap[ik], abs(d__1)) * xk;
s += (d__1 = ap[ik], abs(d__1)) * (d__2 = x[i__ + j *
x_dim1], abs(d__2));
++ik;
}
work[k] = work[k] + (d__1 = ap[kk + k - 1], abs(d__1)) * xk +
s;
kk += k;
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.;
xk = (d__1 = x[k + j * x_dim1], abs(d__1));
work[k] += (d__1 = ap[kk], abs(d__1)) * xk;
ik = kk + 1;
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
work[i__] += (d__1 = ap[ik], abs(d__1)) * xk;
s += (d__1 = ap[ik], abs(d__1)) * (d__2 = x[i__ + j *
x_dim1], abs(d__2));
++ik;
}
work[k] += s;
kk += *n - k + 1;
}
}
s = 0.;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (work[i__] > safe2) {
/* Computing MAX */
d__2 = s, d__3 = (d__1 = work[*n + i__], abs(d__1)) / work[
i__];
s = max(d__2,d__3);
} else {
/* Computing MAX */
d__2 = s, d__3 = ((d__1 = work[*n + i__], abs(d__1)) + safe1)
/ (work[i__] + safe1);
s = max(d__2,d__3);
}
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if */
/* 1) The residual BERR(J) is larger than machine epsilon, and */
/* 2) BERR(J) decreased by at least a factor of 2 during the */
/* last iteration, and */
/* 3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2. <= lstres && count <= 5) {
/* Update solution and try again. */
dsptrs_(uplo, n, &c__1, &afp[1], &ipiv[1], &work[*n + 1], n, info);
daxpy_(n, &c_b14, &work[*n + 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 DLACN2 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 (work[i__] > safe2) {
work[i__] = (d__1 = work[*n + i__], abs(d__1)) + nz * eps *
work[i__];
} else {
work[i__] = (d__1 = work[*n + i__], abs(d__1)) + nz * eps *
work[i__] + safe1;
}
}
kase = 0;
L100:
dlacn2_(n, &work[(*n << 1) + 1], &work[*n + 1], &iwork[1], &ferr[j], &
kase, isave);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(A'). */
dsptrs_(uplo, n, &c__1, &afp[1], &ipiv[1], &work[*n + 1], n,
info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[*n + i__] = work[i__] * work[*n + i__];
}
} else if (kase == 2) {
/* Multiply by inv(A)*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[*n + i__] = work[i__] * work[*n + i__];
}
dsptrs_(uplo, n, &c__1, &afp[1], &ipiv[1], &work[*n + 1], n,
info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = lstres, d__3 = (d__1 = x[i__ + j * x_dim1], abs(d__1));
lstres = max(d__2,d__3);
}
if (lstres != 0.) {
ferr[j] /= lstres;
}
}
return 0;
/* End of DSPRFS */
} /* dsprfs_ */
/* Subroutine */
int dsprfs_(char *uplo, integer *n, integer *nrhs, doublereal *ap, doublereal *afp, integer *ipiv, doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *ferr, doublereal *berr, doublereal *work, integer *iwork, integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3;
doublereal d__1, d__2, d__3;
/* Local variables */
integer i__, j, k;
doublereal s;
integer ik, kk;
doublereal xk;
integer nz;
doublereal eps;
integer kase;
doublereal safe1, safe2;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */
int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *);
integer count;
extern /* Subroutine */
int dspmv_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *);
logical upper;
extern /* Subroutine */
int dlacn2_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *);
extern doublereal dlamch_(char *);
doublereal safmin;
extern /* Subroutine */
int xerbla_(char *, integer *);
doublereal lstres;
extern /* Subroutine */
int dsptrs_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *);
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
--afp;
--ipiv;
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;
--iwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L"))
{
*info = -1;
}
else if (*n < 0)
{
*info = -2;
}
else if (*nrhs < 0)
{
*info = -3;
}
else if (*ldb < max(1,*n))
{
*info = -8;
}
else if (*ldx < max(1,*n))
{
*info = -10;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("DSPRFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0)
{
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
ferr[j] = 0.;
berr[j] = 0.;
/* L10: */
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = dlamch_("Epsilon");
safmin = dlamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
count = 1;
lstres = 3.;
L20: /* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - A * X */
dcopy_(n, &b[j * b_dim1 + 1], &c__1, &work[*n + 1], &c__1);
dspmv_(uplo, n, &c_b12, &ap[1], &x[j * x_dim1 + 1], &c__1, &c_b14, & work[*n + 1], &c__1);
/* Compute componentwise relative backward error from formula */
/* max(i) ( f2c_abs(R(i)) / ( f2c_abs(A)*f2c_abs(X) + f2c_abs(B) )(i) ) */
/* where f2c_abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. If the i-th component of the denominator is less */
/* than SAFE2, then SAFE1 is added to the i-th components of the */
/* numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
work[i__] = (d__1 = b[i__ + j * b_dim1], f2c_abs(d__1));
/* L30: */
}
/* Compute f2c_abs(A)*f2c_abs(X) + f2c_abs(B). */
kk = 1;
if (upper)
{
i__2 = *n;
for (k = 1;
k <= i__2;
++k)
{
s = 0.;
xk = (d__1 = x[k + j * x_dim1], f2c_abs(d__1));
ik = kk;
i__3 = k - 1;
for (i__ = 1;
i__ <= i__3;
++i__)
{
work[i__] += (d__1 = ap[ik], f2c_abs(d__1)) * xk;
s += (d__1 = ap[ik], f2c_abs(d__1)) * (d__2 = x[i__ + j * x_dim1], f2c_abs(d__2));
++ik;
/* L40: */
}
work[k] = work[k] + (d__1 = ap[kk + k - 1], f2c_abs(d__1)) * xk + s;
kk += k;
/* L50: */
}
}
else
{
i__2 = *n;
for (k = 1;
k <= i__2;
++k)
{
s = 0.;
xk = (d__1 = x[k + j * x_dim1], f2c_abs(d__1));
work[k] += (d__1 = ap[kk], f2c_abs(d__1)) * xk;
ik = kk + 1;
i__3 = *n;
for (i__ = k + 1;
i__ <= i__3;
++i__)
{
work[i__] += (d__1 = ap[ik], f2c_abs(d__1)) * xk;
s += (d__1 = ap[ik], f2c_abs(d__1)) * (d__2 = x[i__ + j * x_dim1], f2c_abs(d__2));
++ik;
/* L60: */
}
work[k] += s;
kk += *n - k + 1;
/* L70: */
}
}
s = 0.;
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
if (work[i__] > safe2)
{
/* Computing MAX */
d__2 = s;
d__3 = (d__1 = work[*n + i__], f2c_abs(d__1)) / work[ i__]; // , expr subst
s = max(d__2,d__3);
}
else
{
/* Computing MAX */
d__2 = s;
d__3 = ((d__1 = work[*n + i__], f2c_abs(d__1)) + safe1) / (work[i__] + safe1); // , expr subst
s = max(d__2,d__3);
}
/* L80: */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if */
/* 1) The residual BERR(J) is larger than machine epsilon, and */
/* 2) BERR(J) decreased by at least a factor of 2 during the */
/* last iteration, and */
/* 3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2. <= lstres && count <= 5)
{
/* Update solution and try again. */
dsptrs_(uplo, n, &c__1, &afp[1], &ipiv[1], &work[*n + 1], n, info);
daxpy_(n, &c_b14, &work[*n + 1], &c__1, &x[j * x_dim1 + 1], &c__1) ;
lstres = berr[j];
++count;
goto L20;
}
/* Bound error from formula */
/* norm(X - XTRUE) / norm(X) .le. FERR = */
/* norm( f2c_abs(inv(A))* */
/* ( f2c_abs(R) + NZ*EPS*( f2c_abs(A)*f2c_abs(X)+f2c_abs(B) ))) / norm(X) */
/* where */
/* norm(Z) is the magnitude of the largest component of Z */
/* inv(A) is the inverse of A */
/* f2c_abs(Z) is the componentwise absolute value of the matrix or */
/* vector Z */
/* NZ is the maximum number of nonzeros in any row of A, plus 1 */
/* EPS is machine epsilon */
/* The i-th component of f2c_abs(R)+NZ*EPS*(f2c_abs(A)*f2c_abs(X)+f2c_abs(B)) */
/* is incremented by SAFE1 if the i-th component of */
/* f2c_abs(A)*f2c_abs(X) + f2c_abs(B) is less than SAFE2. */
/* Use DLACN2 to estimate the infinity-norm of the matrix */
/* inv(A) * diag(W), */
/* where W = f2c_abs(R) + NZ*EPS*( f2c_abs(A)*f2c_abs(X)+f2c_abs(B) ))) */
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
if (work[i__] > safe2)
{
work[i__] = (d__1 = work[*n + i__], f2c_abs(d__1)) + nz * eps * work[i__];
}
else
{
work[i__] = (d__1 = work[*n + i__], f2c_abs(d__1)) + nz * eps * work[i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
dlacn2_(n, &work[(*n << 1) + 1], &work[*n + 1], &iwork[1], &ferr[j], & kase, isave);
if (kase != 0)
{
if (kase == 1)
{
/* Multiply by diag(W)*inv(A**T). */
dsptrs_(uplo, n, &c__1, &afp[1], &ipiv[1], &work[*n + 1], n, info);
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
work[*n + i__] = work[i__] * work[*n + i__];
/* L110: */
}
}
else if (kase == 2)
{
/* Multiply by inv(A)*diag(W). */
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
work[*n + i__] = work[i__] * work[*n + i__];
/* L120: */
}
dsptrs_(uplo, n, &c__1, &afp[1], &ipiv[1], &work[*n + 1], n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.;
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
/* Computing MAX */
d__2 = lstres;
d__3 = (d__1 = x[i__ + j * x_dim1], f2c_abs(d__1)); // , expr subst
lstres = max(d__2,d__3);
/* L130: */
}
if (lstres != 0.)
{
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of DSPRFS */
}
/* Subroutine */ int dsprfs_(char *uplo, integer *n, integer *nrhs,
doublereal *ap, doublereal *afp, integer *ipiv, doublereal *b,
integer *ldb, doublereal *x, integer *ldx, doublereal *ferr,
doublereal *berr, doublereal *work, integer *iwork, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
DSPRFS improves the computed solution to a system of linear
equations when the coefficient matrix is symmetric indefinite
and packed, and provides error bounds and backward error estimates
for the solution.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
AFP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
The factored form of the matrix A. AFP contains the block
diagonal matrix D and the multipliers used to obtain the
factor U or L from the factorization A = U*D*U**T or
A = L*D*L**T as computed by DSPTRF, stored as a packed
triangular matrix.
IPIV (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by DSPTRF.
B (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by DSPTRS.
On exit, the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j). The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.
BERR (output) DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in
any element of A or B that makes X(j) an exact solution).
WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
IWORK (workspace) INTEGER 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 */
/* Table of constant values */
static integer c__1 = 1;
static doublereal c_b12 = -1.;
static doublereal c_b14 = 1.;
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3;
doublereal d__1, d__2, d__3;
/* Local variables */
static integer kase;
static doublereal safe1, safe2;
static integer i__, j, k;
static doublereal s;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), daxpy_(integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *);
static integer count;
extern /* Subroutine */ int dspmv_(char *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
integer *);
static logical upper;
static integer ik, kk;
extern doublereal dlamch_(char *);
extern /* Subroutine */ int dlacon_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *);
static doublereal xk;
static integer nz;
static doublereal safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
static doublereal lstres;
extern /* Subroutine */ int dsptrs_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *);
static doublereal eps;
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define x_ref(a_1,a_2) x[(a_2)*x_dim1 + a_1]
--ap;
--afp;
--ipiv;
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;
--iwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < max(1,*n)) {
*info = -8;
} else if (*ldx < max(1,*n)) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSPRFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.;
berr[j] = 0.;
/* L10: */
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = dlamch_("Epsilon");
safmin = dlamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.;
L20:
/* Loop until stopping criterion is satisfied.
Compute residual R = B - A * X */
dcopy_(n, &b_ref(1, j), &c__1, &work[*n + 1], &c__1);
dspmv_(uplo, n, &c_b12, &ap[1], &x_ref(1, j), &c__1, &c_b14, &work[*n
+ 1], &c__1);
/* Compute componentwise relative backward error from formula
max(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) )
where abs(Z) is the componentwise absolute value of the matrix
or vector Z. If the i-th component of the denominator is less
than SAFE2, then SAFE1 is added to the i-th components of the
numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[i__] = (d__1 = b_ref(i__, j), abs(d__1));
/* L30: */
}
/* Compute abs(A)*abs(X) + abs(B). */
kk = 1;
if (upper) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.;
xk = (d__1 = x_ref(k, j), abs(d__1));
ik = kk;
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
work[i__] += (d__1 = ap[ik], abs(d__1)) * xk;
s += (d__1 = ap[ik], abs(d__1)) * (d__2 = x_ref(i__, j),
abs(d__2));
++ik;
/* L40: */
}
work[k] = work[k] + (d__1 = ap[kk + k - 1], abs(d__1)) * xk +
s;
kk += k;
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.;
xk = (d__1 = x_ref(k, j), abs(d__1));
work[k] += (d__1 = ap[kk], abs(d__1)) * xk;
ik = kk + 1;
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
work[i__] += (d__1 = ap[ik], abs(d__1)) * xk;
s += (d__1 = ap[ik], abs(d__1)) * (d__2 = x_ref(i__, j),
abs(d__2));
++ik;
/* L60: */
}
work[k] += s;
kk += *n - k + 1;
/* L70: */
}
}
s = 0.;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (work[i__] > safe2) {
/* Computing MAX */
d__2 = s, d__3 = (d__1 = work[*n + i__], abs(d__1)) / work[
i__];
s = max(d__2,d__3);
} else {
/* Computing MAX */
d__2 = s, d__3 = ((d__1 = work[*n + i__], abs(d__1)) + safe1)
/ (work[i__] + safe1);
s = max(d__2,d__3);
}
/* L80: */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if
1) The residual BERR(J) is larger than machine epsilon, and
2) BERR(J) decreased by at least a factor of 2 during the
last iteration, and
3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2. <= lstres && count <= 5) {
/* Update solution and try again. */
dsptrs_(uplo, n, &c__1, &afp[1], &ipiv[1], &work[*n + 1], n, info);
daxpy_(n, &c_b14, &work[*n + 1], &c__1, &x_ref(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 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 DLACON 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 (work[i__] > safe2) {
work[i__] = (d__1 = work[*n + i__], abs(d__1)) + nz * eps *
work[i__];
} else {
work[i__] = (d__1 = work[*n + i__], abs(d__1)) + nz * eps *
work[i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
dlacon_(n, &work[(*n << 1) + 1], &work[*n + 1], &iwork[1], &ferr[j], &
kase);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(A'). */
dsptrs_(uplo, n, &c__1, &afp[1], &ipiv[1], &work[*n + 1], n,
info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[*n + i__] = work[i__] * work[*n + i__];
/* L110: */
}
} else if (kase == 2) {
/* Multiply by inv(A)*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[*n + i__] = work[i__] * work[*n + i__];
/* L120: */
}
dsptrs_(uplo, n, &c__1, &afp[1], &ipiv[1], &work[*n + 1], n,
info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = lstres, d__3 = (d__1 = x_ref(i__, j), abs(d__1));
lstres = max(d__2,d__3);
/* L130: */
}
if (lstres != 0.) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of DSPRFS */
} /* dsprfs_ */
