/* Subroutine */ int zherfsx_(char *uplo, char *equed, integer *n, integer *
nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *
ldaf, integer *ipiv, doublereal *s, doublecomplex *b, integer *ldb,
doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *berr,
integer *n_err_bnds__, doublereal *err_bnds_norm__, doublereal *
err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex *
work, doublereal *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
err_bnds_comp_dim1, err_bnds_comp_offset, i__1;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal illrcond_thresh__, unstable_thresh__, err_lbnd__;
integer ref_type__;
integer j;
doublereal rcond_tmp__;
integer prec_type__;
doublereal cwise_wrong__;
extern /* Subroutine */ int zla_herfsx_extended__(integer *, char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *, logical *, doublereal *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
doublecomplex *, doublecomplex *, doublereal *, integer *,
doublereal *, doublereal *, logical *, integer *, ftnlen);
char norm[1];
logical ignore_cwise__;
extern logical lsame_(char *, char *);
doublereal anorm;
logical rcequ;
extern doublereal zla_hercond_c__(char *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, integer *, doublereal *,
logical *, integer *, doublecomplex *, doublereal *, ftnlen),
zla_hercond_x__(char *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, doublereal *, ftnlen), dlamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *,
integer *, doublereal *);
extern /* Subroutine */ int zhecon_(char *, integer *, doublecomplex *,
integer *, integer *, doublereal *, doublereal *, doublecomplex *,
integer *);
extern integer ilaprec_(char *);
integer ithresh, n_norms__;
doublereal rthresh;
/* -- LAPACK routine (version 3.2.1) -- */
/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/* -- Jason Riedy of Univ. of California Berkeley. -- */
/* -- April 2009 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley and NAG Ltd. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* Purpose */
/* ======= */
/* ZHERFSX improves the computed solution to a system of linear */
/* equations when the coefficient matrix is Hermitian indefinite, and */
/* provides error bounds and backward error estimates for the */
/* solution. In addition to normwise error bound, the code provides */
/* maximum componentwise error bound if possible. See comments for */
/* ERR_BNDS_NORM and ERR_BNDS_COMP for details of the error bounds. */
/* The original system of linear equations may have been equilibrated */
/* before calling this routine, as described by arguments EQUED and S */
/* below. In this case, the solution and error bounds returned are */
/* for the original unequilibrated system. */
/* Arguments */
/* ========= */
/* Some optional parameters are bundled in the PARAMS array. These */
/* settings determine how refinement is performed, but often the */
/* defaults are acceptable. If the defaults are acceptable, users */
/* can pass NPARAMS = 0 which prevents the source code from accessing */
/* the PARAMS argument. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* EQUED (input) CHARACTER*1 */
/* Specifies the form of equilibration that was done to A */
/* before calling this routine. This is needed to compute */
/* the solution and error bounds correctly. */
/* = 'N': No equilibration */
/* = 'Y': Both row and column equilibration, i.e., A has been */
/* replaced by diag(S) * A * diag(S). */
/* The right hand side B has been changed accordingly. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* A (input) COMPLEX*16 array, dimension (LDA,N) */
/* The symmetric matrix A. If UPLO = 'U', the leading N-by-N */
/* upper triangular part of A contains the upper triangular */
/* part of the matrix A, and the strictly lower triangular */
/* part of A is not referenced. If UPLO = 'L', the leading */
/* N-by-N lower triangular part of A contains the lower */
/* triangular part of the matrix A, and the strictly upper */
/* triangular part of A is not referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input) COMPLEX*16 array, dimension (LDAF,N) */
/* The factored form of the matrix A. AF 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 DSYTRF. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* IPIV (input) INTEGER array, dimension (N) */
/* Details of the interchanges and the block structure of D */
/* as determined by DSYTRF. */
/* S (input or output) DOUBLE PRECISION array, dimension (N) */
/* The scale factors for A. If EQUED = 'Y', A is multiplied on */
/* the left and right by diag(S). 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. If S is output, each */
/* element of S is a power of the radix. If S is input, each element */
/* of S should be a power of the radix to ensure a reliable solution */
/* and error estimates. Scaling by powers of the radix does not cause */
/* rounding errors unless the result underflows or overflows. */
/* Rounding errors during scaling lead to refining with a matrix that */
/* is not equivalent to the input matrix, producing error estimates */
/* that may not be reliable. */
/* B (input) COMPLEX*16 array, dimension (LDB,NRHS) */
/* The right hand side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (input/output) COMPLEX*16 array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by DGETRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* RCOND (output) DOUBLE PRECISION */
/* Reciprocal scaled condition number. This is an estimate of the */
/* reciprocal Skeel condition number of the matrix A after */
/* equilibration (if done). If this is less than the machine */
/* precision (in particular, if it is zero), the matrix is singular */
/* to working precision. Note that the error may still be small even */
/* if this number is very small and the matrix appears ill- */
/* conditioned. */
/* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* Componentwise relative backward error. This is 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). */
/* N_ERR_BNDS (input) INTEGER */
/* Number of error bounds to return for each right hand side */
/* and each type (normwise or componentwise). See ERR_BNDS_NORM and */
/* ERR_BNDS_COMP below. */
/* ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* normwise relative error, which is defined as follows: */
/* Normwise relative error in the ith solution vector: */
/* max_j (abs(XTRUE(j,i) - X(j,i))) */
/* ------------------------------ */
/* max_j abs(X(j,i)) */
/* The array is indexed by the type of error information as described */
/* below. There currently are up to three pieces of information */
/* returned. */
/* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_NORM(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * dlamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * dlamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated normwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * dlamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*A, where S scales each row by a power of the */
/* radix so all absolute row sums of Z are approximately 1. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* componentwise relative error, which is defined as follows: */
/* Componentwise relative error in the ith solution vector: */
/* abs(XTRUE(j,i) - X(j,i)) */
/* max_j ---------------------- */
/* abs(X(j,i)) */
/* The array is indexed by the right-hand side i (on which the */
/* componentwise relative error depends), and the type of error */
/* information as described below. There currently are up to three */
/* pieces of information returned for each right-hand side. If */
/* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */
/* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */
/* the first (:,N_ERR_BNDS) entries are returned. */
/* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_COMP(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * dlamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * dlamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated componentwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * dlamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*(A*diag(x)), where x is the solution for the */
/* current right-hand side and S scales each row of */
/* A*diag(x) by a power of the radix so all absolute row */
/* sums of Z are approximately 1. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* NPARAMS (input) INTEGER */
/* Specifies the number of parameters set in PARAMS. If .LE. 0, the */
/* PARAMS array is never referenced and default values are used. */
/* PARAMS (input / output) DOUBLE PRECISION array, dimension NPARAMS */
/* Specifies algorithm parameters. If an entry is .LT. 0.0, then */
/* that entry will be filled with default value used for that */
/* parameter. Only positions up to NPARAMS are accessed; defaults */
/* are used for higher-numbered parameters. */
/* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */
/* refinement or not. */
/* Default: 1.0D+0 */
/* = 0.0 : No refinement is performed, and no error bounds are */
/* computed. */
/* = 1.0 : Use the double-precision refinement algorithm, */
/* possibly with doubled-single computations if the */
/* compilation environment does not support DOUBLE */
/* PRECISION. */
/* (other values are reserved for future use) */
/* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */
/* computations allowed for refinement. */
/* Default: 10 */
/* Aggressive: Set to 100 to permit convergence using approximate */
/* factorizations or factorizations other than LU. If */
/* the factorization uses a technique other than */
/* Gaussian elimination, the guarantees in */
/* err_bnds_norm and err_bnds_comp may no longer be */
/* trustworthy. */
/* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */
/* will attempt to find a solution with small componentwise */
/* relative error in the double-precision algorithm. Positive */
/* is true, 0.0 is false. */
/* Default: 1.0 (attempt componentwise convergence) */
/* WORK (workspace) COMPLEX*16 array, dimension (2*N) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: Successful exit. The solution to every right-hand side is */
/* guaranteed. */
/* < 0: If INFO = -i, the i-th argument had an illegal value */
/* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */
/* has been completed, but the factor U is exactly singular, so */
/* the solution and error bounds could not be computed. RCOND = 0 */
/* is returned. */
/* = N+J: The solution corresponding to the Jth right-hand side is */
/* not guaranteed. The solutions corresponding to other right- */
/* hand sides K with K > J may not be guaranteed as well, but */
/* only the first such right-hand side is reported. If a small */
/* componentwise error is not requested (PARAMS(3) = 0.0) then */
/* the Jth right-hand side is the first with a normwise error */
/* bound that is not guaranteed (the smallest J such */
/* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */
/* the Jth right-hand side is the first with either a normwise or */
/* componentwise error bound that is not guaranteed (the smallest */
/* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */
/* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */
/* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */
/* about all of the right-hand sides check ERR_BNDS_NORM or */
/* ERR_BNDS_COMP. */
/* ================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Check the input parameters. */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1;
err_bnds_norm__ -= err_bnds_norm_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
--s;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--berr;
--params;
--work;
--rwork;
/* Function Body */
*info = 0;
ref_type__ = 1;
if (*nparams >= 1) {
if (params[1] < 0.) {
params[1] = 1.;
} else {
ref_type__ = (integer) params[1];
}
}
/* Set default parameters. */
illrcond_thresh__ = (doublereal) (*n) * dlamch_("Epsilon");
ithresh = 10;
rthresh = .5;
unstable_thresh__ = .25;
ignore_cwise__ = FALSE_;
if (*nparams >= 2) {
if (params[2] < 0.) {
params[2] = (doublereal) ithresh;
} else {
ithresh = (integer) params[2];
}
}
if (*nparams >= 3) {
if (params[3] < 0.) {
if (ignore_cwise__) {
params[3] = 0.;
} else {
params[3] = 1.;
}
} else {
ignore_cwise__ = params[3] == 0.;
}
}
if (ref_type__ == 0 || *n_err_bnds__ == 0) {
n_norms__ = 0;
} else if (ignore_cwise__) {
n_norms__ = 1;
} else {
n_norms__ = 2;
}
rcequ = lsame_(equed, "Y");
/* Test input parameters. */
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! rcequ && ! lsame_(equed, "N")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else if (*ldaf < max(1,*n)) {
*info = -8;
} else if (*ldb < max(1,*n)) {
*info = -11;
} else if (*ldx < max(1,*n)) {
*info = -13;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHERFSX", &i__1);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *nrhs == 0) {
*rcond = 1.;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
berr[j] = 0.;
if (*n_err_bnds__ >= 1) {
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.;
} else if (*n_err_bnds__ >= 2) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.;
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.;
} else if (*n_err_bnds__ >= 3) {
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.;
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.;
}
}
return 0;
}
/* Default to failure. */
*rcond = 0.;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
berr[j] = 1.;
if (*n_err_bnds__ >= 1) {
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.;
} else if (*n_err_bnds__ >= 2) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.;
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.;
} else if (*n_err_bnds__ >= 3) {
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.;
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.;
}
}
/* Compute the norm of A and the reciprocal of the condition */
/* number of A. */
*(unsigned char *)norm = 'I';
anorm = zlanhe_(norm, uplo, n, &a[a_offset], lda, &rwork[1]);
zhecon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1],
info);
/* Perform refinement on each right-hand side */
if (ref_type__ != 0) {
prec_type__ = ilaprec_("E");
zla_herfsx_extended__(&prec_type__, uplo, n, nrhs, &a[a_offset], lda,
&af[af_offset], ldaf, &ipiv[1], &rcequ, &s[1], &b[b_offset],
ldb, &x[x_offset], ldx, &berr[1], &n_norms__, &
err_bnds_norm__[err_bnds_norm_offset], &err_bnds_comp__[
err_bnds_comp_offset], &work[1], &rwork[1], &work[*n + 1],
(doublecomplex *)(&rwork[1]), rcond, &ithresh, &rthresh, &unstable_thresh__, &
ignore_cwise__, info, (ftnlen)1);
}
/* Computing MAX */
d__1 = 10., d__2 = sqrt((doublereal) (*n));
err_lbnd__ = max(d__1,d__2) * dlamch_("Epsilon");
if (*n_err_bnds__ >= 1 && n_norms__ >= 1) {
/* Compute scaled normwise condition number cond(A*C). */
if (rcequ) {
rcond_tmp__ = zla_hercond_c__(uplo, n, &a[a_offset], lda, &af[
af_offset], ldaf, &ipiv[1], &s[1], &c_true, info, &work[1]
, &rwork[1], (ftnlen)1);
} else {
rcond_tmp__ = zla_hercond_c__(uplo, n, &a[a_offset], lda, &af[
af_offset], ldaf, &ipiv[1], &s[1], &c_false, info, &work[
1], &rwork[1], (ftnlen)1);
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
/* Cap the error at 1.0. */
if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1
<< 1)] > 1.) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.;
}
/* Threshold the error (see LAWN). */
if (rcond_tmp__ < illrcond_thresh__) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.;
err_bnds_norm__[j + err_bnds_norm_dim1] = 0.;
if (*info <= *n) {
*info = *n + j;
}
} else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] <
err_lbnd__) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__;
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.;
}
/* Save the condition number. */
if (*n_err_bnds__ >= 3) {
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__;
}
}
}
if (*n_err_bnds__ >= 1 && n_norms__ >= 2) {
/* Compute componentwise condition number cond(A*diag(Y(:,J))) for */
/* each right-hand side using the current solution as an estimate of */
/* the true solution. If the componentwise error estimate is too */
/* large, then the solution is a lousy estimate of truth and the */
/* estimated RCOND may be too optimistic. To avoid misleading users, */
/* the inverse condition number is set to 0.0 when the estimated */
/* cwise error is at least CWISE_WRONG. */
cwise_wrong__ = sqrt(dlamch_("Epsilon"));
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] <
cwise_wrong__) {
rcond_tmp__ = zla_hercond_x__(uplo, n, &a[a_offset], lda, &af[
af_offset], ldaf, &ipiv[1], &x[j * x_dim1 + 1], info,
&work[1], &rwork[1], (ftnlen)1);
} else {
rcond_tmp__ = 0.;
}
/* Cap the error at 1.0. */
if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1
<< 1)] > 1.) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.;
}
/* Threshold the error (see LAWN). */
if (rcond_tmp__ < illrcond_thresh__) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.;
err_bnds_comp__[j + err_bnds_comp_dim1] = 0.;
if (params[3] == 1. && *info < *n + j) {
*info = *n + j;
}
} else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] <
err_lbnd__) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.;
}
/* Save the condition number. */
if (*n_err_bnds__ >= 3) {
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__;
}
}
}
return 0;
/* End of ZHERFSX */
} /* zherfsx_ */
/* Subroutine */ int zchkhe_(logical *dotype, integer *nn, integer *nval,
integer *nnb, integer *nbval, integer *nns, integer *nsval,
doublereal *thresh, logical *tsterr, integer *nmax, doublecomplex *a,
doublecomplex *afac, doublecomplex *ainv, doublecomplex *b,
doublecomplex *x, doublecomplex *xact, doublecomplex *work,
doublereal *rwork, integer *iwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char uplos[1*2] = "U" "L";
/* Format strings */
static char fmt_9999[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, "
"NB =\002,i4,\002, type \002,i2,\002, test \002,i2,\002, ratio "
"=\002,g12.5)";
static char fmt_9998[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, "
"NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g"
"12.5)";
static char fmt_9997[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002"
",\002,10x,\002 type \002,i2,\002, test(\002,i2,\002) =\002,g12.5)"
;
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, j, k, n, i1, i2, nb, in, kl, ku, nt, lda, inb, ioff, mode,
imat, info;
char path[3], dist[1];
integer irhs, nrhs;
char uplo[1], type__[1];
integer nrun;
extern /* Subroutine */ int alahd_(integer *, char *);
integer nfail, iseed[4];
extern doublereal dget06_(doublereal *, doublereal *);
doublereal rcond;
integer nimat;
extern /* Subroutine */ int zhet01_(char *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *);
doublereal anorm;
extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *
);
integer iuplo, izero, nerrs, lwork;
extern /* Subroutine */ int zpot02_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *),
zpot03_(char *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublereal *), zpot05_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *
, integer *, doublecomplex *, integer *, doublecomplex *, integer
*, doublereal *, doublereal *, doublereal *);
logical zerot;
char xtype[1];
extern /* Subroutine */ int zlatb4_(char *, integer *, integer *, integer
*, char *, integer *, integer *, doublereal *, integer *,
doublereal *, char *), alaerh_(char *,
char *, integer *, integer *, char *, integer *, integer *,
integer *, integer *, integer *, integer *, integer *, integer *,
integer *);
doublereal rcondc;
extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *,
integer *, doublereal *);
extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer
*, integer *);
doublereal cndnum;
extern /* Subroutine */ int zlaipd_(integer *, doublecomplex *, integer *,
integer *), zhecon_(char *, integer *, doublecomplex *, integer *
, integer *, doublereal *, doublereal *, doublecomplex *, integer
*);
logical trfcon;
extern /* Subroutine */ int xlaenv_(integer *, integer *), zerrhe_(char *,
integer *), zherfs_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zhetrf_(char *, integer *, doublecomplex *,
integer *, integer *, doublecomplex *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *), zhetri_(char *,
integer *, doublecomplex *, integer *, integer *, doublecomplex *,
integer *), zlarhs_(char *, char *, char *, char *,
integer *, integer *, integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *, integer *), zlatms_(integer *, integer *, char *, integer *,
char *, doublereal *, integer *, doublereal *, doublereal *,
integer *, integer *, char *, doublecomplex *, integer *,
doublecomplex *, integer *);
doublereal result[8];
extern /* Subroutine */ int zhetrs_(char *, integer *, integer *,
doublecomplex *, integer *, integer *, doublecomplex *, integer *,
integer *);
/* Fortran I/O blocks */
static cilist io___39 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___44 = { 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 */
/* ======= */
/* ZCHKHE tests ZHETRF, -TRI, -TRS, -RFS, and -CON. */
/* Arguments */
/* ========= */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* The matrix types to be used for testing. Matrices of type j */
/* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix dimension N. */
/* NNB (input) INTEGER */
/* The number of values of NB contained in the vector NBVAL. */
/* NBVAL (input) INTEGER array, dimension (NBVAL) */
/* The values of the blocksize NB. */
/* NNS (input) INTEGER */
/* The number of values of NRHS contained in the vector NSVAL. */
/* NSVAL (input) INTEGER array, dimension (NNS) */
/* The values of the number of right hand sides NRHS. */
/* THRESH (input) DOUBLE PRECISION */
/* The threshold value for the test ratios. A result is */
/* included in the output file if RESULT >= THRESH. To have */
/* every test ratio printed, use THRESH = 0. */
/* TSTERR (input) LOGICAL */
/* Flag that indicates whether error exits are to be tested. */
/* NMAX (input) INTEGER */
/* The maximum value permitted for N, used in dimensioning the */
/* work arrays. */
/* A (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* AFAC (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* AINV (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* B (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* where NSMAX is the largest entry in NSVAL. */
/* X (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* XACT (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* WORK (workspace) COMPLEX*16 array, dimension */
/* (NMAX*max(3,NSMAX)) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension */
/* (max(NMAX,2*NSMAX)) */
/* IWORK (workspace) INTEGER array, dimension (NMAX) */
/* 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 */
--iwork;
--rwork;
--work;
--xact;
--x;
--b;
--ainv;
--afac;
--a;
--nsval;
--nbval;
--nval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "HE", (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) {
zerrhe_(path, nout);
}
infoc_1.infot = 0;
/* Do for each value of N in NVAL */
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
n = nval[in];
lda = max(n,1);
*(unsigned char *)xtype = 'N';
nimat = 10;
if (n <= 0) {
nimat = 1;
}
izero = 0;
i__2 = nimat;
for (imat = 1; imat <= i__2; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L170;
}
/* Skip types 3, 4, 5, or 6 if the matrix size is too small. */
zerot = imat >= 3 && imat <= 6;
if (zerot && n < imat - 2) {
goto L170;
}
/* Do first for UPLO = 'U', then for UPLO = 'L' */
for (iuplo = 1; iuplo <= 2; ++iuplo) {
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
/* Set up parameters with ZLATB4 and generate a test matrix */
/* with ZLATMS. */
zlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode,
&cndnum, dist);
s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)6, (ftnlen)6);
zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &
cndnum, &anorm, &kl, &ku, uplo, &a[1], &lda, &work[1],
&info);
/* Check error code from ZLATMS. */
if (info != 0) {
alaerh_(path, "ZLATMS", &info, &c__0, uplo, &n, &n, &c_n1,
&c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
goto L160;
}
/* For types 3-6, zero one or more rows and columns of */
/* the matrix to test that INFO is returned correctly. */
if (zerot) {
if (imat == 3) {
izero = 1;
} else if (imat == 4) {
izero = n;
} else {
izero = n / 2 + 1;
}
if (imat < 6) {
/* Set row and column IZERO to zero. */
if (iuplo == 1) {
ioff = (izero - 1) * lda;
i__3 = izero - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = ioff + i__;
a[i__4].r = 0., a[i__4].i = 0.;
/* L20: */
}
ioff += izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
i__4 = ioff;
a[i__4].r = 0., a[i__4].i = 0.;
ioff += lda;
/* L30: */
}
} else {
ioff = izero;
i__3 = izero - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = ioff;
a[i__4].r = 0., a[i__4].i = 0.;
ioff += lda;
/* L40: */
}
ioff -= izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
i__4 = ioff + i__;
a[i__4].r = 0., a[i__4].i = 0.;
/* L50: */
}
}
} else {
ioff = 0;
if (iuplo == 1) {
/* Set the first IZERO rows and columns to zero. */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i2 = min(j,izero);
i__4 = i2;
for (i__ = 1; i__ <= i__4; ++i__) {
i__5 = ioff + i__;
a[i__5].r = 0., a[i__5].i = 0.;
/* L60: */
}
ioff += lda;
/* L70: */
}
} else {
/* Set the last IZERO rows and columns to zero. */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i1 = max(j,izero);
i__4 = n;
for (i__ = i1; i__ <= i__4; ++i__) {
i__5 = ioff + i__;
a[i__5].r = 0., a[i__5].i = 0.;
/* L80: */
}
ioff += lda;
/* L90: */
}
}
}
} else {
izero = 0;
}
/* Set the imaginary part of the diagonals. */
i__3 = lda + 1;
zlaipd_(&n, &a[1], &i__3, &c__0);
/* Do for each value of NB in NBVAL */
i__3 = *nnb;
for (inb = 1; inb <= i__3; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
/* Compute the L*D*L' or U*D*U' factorization of the */
/* matrix. */
zlacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda);
lwork = max(2,nb) * lda;
s_copy(srnamc_1.srnamt, "ZHETRF", (ftnlen)6, (ftnlen)6);
zhetrf_(uplo, &n, &afac[1], &lda, &iwork[1], &ainv[1], &
lwork, &info);
/* Adjust the expected value of INFO to account for */
/* pivoting. */
k = izero;
if (k > 0) {
L100:
if (iwork[k] < 0) {
if (iwork[k] != -k) {
k = -iwork[k];
goto L100;
}
} else if (iwork[k] != k) {
k = iwork[k];
goto L100;
}
}
/* Check error code from ZHETRF. */
if (info != k) {
alaerh_(path, "ZHETRF", &info, &k, uplo, &n, &n, &
c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout);
}
if (info != 0) {
trfcon = TRUE_;
} else {
trfcon = FALSE_;
}
/* + TEST 1 */
/* Reconstruct matrix from factors and compute residual. */
zhet01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &iwork[1],
&ainv[1], &lda, &rwork[1], result);
nt = 1;
/* + TEST 2 */
/* Form the inverse and compute the residual. */
if (inb == 1 && ! trfcon) {
zlacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda);
s_copy(srnamc_1.srnamt, "ZHETRI", (ftnlen)6, (ftnlen)
6);
zhetri_(uplo, &n, &ainv[1], &lda, &iwork[1], &work[1],
&info);
/* Check error code from ZHETRI. */
if (info != 0) {
alaerh_(path, "ZHETRI", &info, &c_n1, uplo, &n, &
n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &
nerrs, nout);
}
zpot03_(uplo, &n, &a[1], &lda, &ainv[1], &lda, &work[
1], &lda, &rwork[1], &rcondc, &result[1]);
nt = 2;
}
/* Print information about the tests that did not pass */
/* the threshold. */
i__4 = nt;
for (k = 1; k <= i__4; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___39.ciunit = *nout;
s_wsfe(&io___39);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&nb, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
sizeof(doublereal));
e_wsfe();
++nfail;
}
/* L110: */
}
nrun += nt;
/* Skip the other tests if this is not the first block */
/* size. */
if (inb > 1) {
goto L150;
}
/* Do only the condition estimate if INFO is not 0. */
if (trfcon) {
rcondc = 0.;
goto L140;
}
i__4 = *nns;
for (irhs = 1; irhs <= i__4; ++irhs) {
nrhs = nsval[irhs];
/* + TEST 3 */
/* Solve and compute residual for A * X = B. */
s_copy(srnamc_1.srnamt, "ZLARHS", (ftnlen)6, (ftnlen)
6);
zlarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, &
nrhs, &a[1], &lda, &xact[1], &lda, &b[1], &
lda, iseed, &info);
zlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda);
s_copy(srnamc_1.srnamt, "ZHETRS", (ftnlen)6, (ftnlen)
6);
zhetrs_(uplo, &n, &nrhs, &afac[1], &lda, &iwork[1], &
x[1], &lda, &info);
/* Check error code from ZHETRS. */
if (info != 0) {
alaerh_(path, "ZHETRS", &info, &c__0, uplo, &n, &
n, &c_n1, &c_n1, &nrhs, &imat, &nfail, &
nerrs, nout);
}
zlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &
lda);
zpot02_(uplo, &n, &nrhs, &a[1], &lda, &x[1], &lda, &
work[1], &lda, &rwork[1], &result[2]);
/* + TEST 4 */
/* Check solution from generated exact solution. */
zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[3]);
/* + TESTS 5, 6, and 7 */
/* Use iterative refinement to improve the solution. */
s_copy(srnamc_1.srnamt, "ZHERFS", (ftnlen)6, (ftnlen)
6);
zherfs_(uplo, &n, &nrhs, &a[1], &lda, &afac[1], &lda,
&iwork[1], &b[1], &lda, &x[1], &lda, &rwork[1]
, &rwork[nrhs + 1], &work[1], &rwork[(nrhs <<
1) + 1], &info);
/* Check error code from ZHERFS. */
if (info != 0) {
alaerh_(path, "ZHERFS", &info, &c__0, uplo, &n, &
n, &c_n1, &c_n1, &nrhs, &imat, &nfail, &
nerrs, nout);
}
zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[4]);
zpot05_(uplo, &n, &nrhs, &a[1], &lda, &b[1], &lda, &x[
1], &lda, &xact[1], &lda, &rwork[1], &rwork[
nrhs + 1], &result[5]);
/* Print information about the tests that did not pass */
/* the threshold. */
for (k = 3; k <= 7; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___42.ciunit = *nout;
s_wsfe(&io___42);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&nrhs, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
sizeof(doublereal));
e_wsfe();
++nfail;
}
/* L120: */
}
nrun += 5;
/* L130: */
}
/* + TEST 8 */
/* Get an estimate of RCOND = 1/CNDNUM. */
L140:
anorm = zlanhe_("1", uplo, &n, &a[1], &lda, &rwork[1]);
s_copy(srnamc_1.srnamt, "ZHECON", (ftnlen)6, (ftnlen)6);
zhecon_(uplo, &n, &afac[1], &lda, &iwork[1], &anorm, &
rcond, &work[1], &info);
/* Check error code from ZHECON. */
if (info != 0) {
alaerh_(path, "ZHECON", &info, &c__0, uplo, &n, &n, &
c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs,
nout);
}
result[7] = dget06_(&rcond, &rcondc);
/* Print information about the tests that did not pass */
/* the threshold. */
if (result[7] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___44.ciunit = *nout;
s_wsfe(&io___44);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&c__8, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
++nrun;
L150:
;
}
L160:
;
}
L170:
;
}
/* L180: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of ZCHKHE */
} /* zchkhe_ */
int main(void)
{
/* Local scalars */
char uplo, uplo_i;
lapack_int n, n_i;
lapack_int lda, lda_i;
lapack_int lda_r;
double anorm, anorm_i;
double rcond, rcond_i;
lapack_int info, info_i;
lapack_int i;
int failed;
/* Local arrays */
lapack_complex_double *a = NULL, *a_i = NULL;
lapack_int *ipiv = NULL, *ipiv_i = NULL;
lapack_complex_double *work = NULL, *work_i = NULL;
lapack_complex_double *a_r = NULL;
/* Iniitialize the scalar parameters */
init_scalars_zhecon( &uplo, &n, &lda, &anorm );
lda_r = n+2;
uplo_i = uplo;
n_i = n;
lda_i = lda;
anorm_i = anorm;
/* Allocate memory for the LAPACK routine arrays */
a = (lapack_complex_double *)
LAPACKE_malloc( lda*n * sizeof(lapack_complex_double) );
ipiv = (lapack_int *)LAPACKE_malloc( n * sizeof(lapack_int) );
work = (lapack_complex_double *)
LAPACKE_malloc( 2*n * sizeof(lapack_complex_double) );
/* Allocate memory for the C interface function arrays */
a_i = (lapack_complex_double *)
LAPACKE_malloc( lda*n * sizeof(lapack_complex_double) );
ipiv_i = (lapack_int *)LAPACKE_malloc( n * sizeof(lapack_int) );
work_i = (lapack_complex_double *)
LAPACKE_malloc( 2*n * sizeof(lapack_complex_double) );
/* Allocate memory for the row-major arrays */
a_r = (lapack_complex_double *)
LAPACKE_malloc( n*(n+2) * sizeof(lapack_complex_double) );
/* Initialize input arrays */
init_a( lda*n, a );
init_ipiv( n, ipiv );
init_work( 2*n, work );
/* Call the LAPACK routine */
zhecon_( &uplo, &n, a, &lda, ipiv, &anorm, &rcond, work, &info );
/* Initialize input data, call the column-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv[i];
}
for( i = 0; i < 2*n; i++ ) {
work_i[i] = work[i];
}
info_i = LAPACKE_zhecon_work( LAPACK_COL_MAJOR, uplo_i, n_i, a_i, lda_i,
ipiv_i, anorm_i, &rcond_i, work_i );
failed = compare_zhecon( rcond, rcond_i, info, info_i );
if( failed == 0 ) {
printf( "PASSED: column-major middle-level interface to zhecon\n" );
} else {
printf( "FAILED: column-major middle-level interface to zhecon\n" );
}
/* Initialize input data, call the column-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv[i];
}
for( i = 0; i < 2*n; i++ ) {
work_i[i] = work[i];
}
info_i = LAPACKE_zhecon( LAPACK_COL_MAJOR, uplo_i, n_i, a_i, lda_i, ipiv_i,
anorm_i, &rcond_i );
failed = compare_zhecon( rcond, rcond_i, info, info_i );
if( failed == 0 ) {
printf( "PASSED: column-major high-level interface to zhecon\n" );
} else {
printf( "FAILED: column-major high-level interface to zhecon\n" );
}
/* Initialize input data, call the row-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv[i];
}
for( i = 0; i < 2*n; i++ ) {
work_i[i] = work[i];
}
LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 );
info_i = LAPACKE_zhecon_work( LAPACK_ROW_MAJOR, uplo_i, n_i, a_r, lda_r,
ipiv_i, anorm_i, &rcond_i, work_i );
failed = compare_zhecon( rcond, rcond_i, info, info_i );
if( failed == 0 ) {
printf( "PASSED: row-major middle-level interface to zhecon\n" );
} else {
printf( "FAILED: row-major middle-level interface to zhecon\n" );
}
/* Initialize input data, call the row-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv[i];
}
for( i = 0; i < 2*n; i++ ) {
work_i[i] = work[i];
}
/* Init row_major arrays */
LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 );
info_i = LAPACKE_zhecon( LAPACK_ROW_MAJOR, uplo_i, n_i, a_r, lda_r, ipiv_i,
anorm_i, &rcond_i );
failed = compare_zhecon( rcond, rcond_i, info, info_i );
if( failed == 0 ) {
printf( "PASSED: row-major high-level interface to zhecon\n" );
} else {
printf( "FAILED: row-major high-level interface to zhecon\n" );
}
/* Release memory */
if( a != NULL ) {
LAPACKE_free( a );
}
if( a_i != NULL ) {
LAPACKE_free( a_i );
}
if( a_r != NULL ) {
LAPACKE_free( a_r );
}
if( ipiv != NULL ) {
LAPACKE_free( ipiv );
}
if( ipiv_i != NULL ) {
LAPACKE_free( ipiv_i );
}
if( work != NULL ) {
LAPACKE_free( work );
}
if( work_i != NULL ) {
LAPACKE_free( work_i );
}
return 0;
}
/* Subroutine */ int zhesvx_(char *fact, char *uplo, integer *n, integer *
nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *
ldaf, integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x,
integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr,
doublecomplex *work, integer *lwork, doublereal *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2;
/* Local variables */
integer nb;
extern logical lsame_(char *, char *);
doublereal anorm;
extern doublereal dlamch_(char *);
logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *,
integer *, doublereal *);
extern /* Subroutine */ int zhecon_(char *, integer *, doublecomplex *,
integer *, integer *, doublereal *, doublereal *, doublecomplex *,
integer *), zherfs_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zhetrf_(char *, integer *, doublecomplex *,
integer *, integer *, doublecomplex *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *), zhetrs_(char *,
integer *, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, integer *, integer *);
integer lwkopt;
logical lquery;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZHESVX uses the diagonal pivoting factorization to compute the */
/* solution to a complex system of linear equations A * X = B, */
/* where A is an N-by-N Hermitian 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 diagonal pivoting method is used to factor A. */
/* The form of the factorization is */
/* A = U * D * U**H, if UPLO = 'U', or */
/* A = L * D * L**H, if UPLO = 'L', */
/* where U (or L) is a product of permutation and unit upper (lower) */
/* triangular matrices, and D is Hermitian 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, AF and IPIV contain the factored form */
/* of A. A, AF and IPIV will not be modified. */
/* = 'N': The matrix A will be copied to AF and factored. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* A (input) COMPLEX*16 array, dimension (LDA,N) */
/* The Hermitian matrix A. If UPLO = 'U', the leading N-by-N */
/* upper triangular part of A contains the upper triangular part */
/* of the matrix A, and the strictly lower triangular part of A */
/* is not referenced. If UPLO = 'L', the leading N-by-N lower */
/* triangular part of A contains the lower triangular part of */
/* the matrix A, and the strictly upper triangular part of A is */
/* not referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input or output) COMPLEX*16 array, dimension (LDAF,N) */
/* If FACT = 'F', then AF 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**H or A = L*D*L**H as computed by ZHETRF. */
/* If FACT = 'N', then AF is an output argument and on exit */
/* returns the block diagonal matrix D and the multipliers used */
/* to obtain the factor U or L from the factorization */
/* A = U*D*U**H or A = L*D*L**H. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* 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 ZHETRF. */
/* 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 ZHETRF. */
/* B (input) COMPLEX*16 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) COMPLEX*16 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/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The length of WORK. LWORK >= max(1,2*N), and for best */
/* performance, when FACT = 'N', LWORK >= max(1,2*N,N*NB), where */
/* NB is the optimal blocksize for ZHETRF. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, and i is */
/* <= N: 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. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--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;
--rwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
lquery = *lwork == -1;
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 (*lda < max(1,*n)) {
*info = -6;
} else if (*ldaf < max(1,*n)) {
*info = -8;
} else if (*ldb < max(1,*n)) {
*info = -11;
} else if (*ldx < max(1,*n)) {
*info = -13;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = 1, i__2 = *n << 1;
if (*lwork < max(i__1,i__2) && ! lquery) {
*info = -18;
}
}
if (*info == 0) {
/* Computing MAX */
i__1 = 1, i__2 = *n << 1;
lwkopt = max(i__1,i__2);
if (nofact) {
nb = ilaenv_(&c__1, "ZHETRF", uplo, n, &c_n1, &c_n1, &c_n1);
/* Computing MAX */
i__1 = lwkopt, i__2 = *n * nb;
lwkopt = max(i__1,i__2);
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHESVX", &i__1);
return 0;
} else if (lquery) {
return 0;
}
if (nofact) {
/* Compute the factorization A = U*D*U' or A = L*D*L'. */
zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
zhetrf_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &work[1], lwork,
info);
/* Return if INFO is non-zero. */
if (*info > 0) {
*rcond = 0.;
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = zlanhe_("I", uplo, n, &a[a_offset], lda, &rwork[1]);
/* Compute the reciprocal of the condition number of A. */
zhecon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1],
info);
/* Compute the solution vectors X. */
zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
zhetrs_(uplo, n, nrhs, &af[af_offset], ldaf, &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. */
zherfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1],
&b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1]
, &rwork[1], info);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < dlamch_("Epsilon")) {
*info = *n + 1;
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZHESVX */
} /* zhesvx_ */
