/* Subroutine */
int cla_syrfsx_extended_(integer *prec_type__, char *uplo, integer *n, integer *nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer *ipiv, logical *colequ, real *c__, complex *b, integer *ldb, complex *y, integer *ldy, real *berr_out__, integer * n_norms__, real *err_bnds_norm__, real *err_bnds_comp__, complex *res, real *ayb, complex *dy, complex *y_tail__, real *rcond, integer * ithresh, real *rthresh, real *dz_ub__, logical *ignore_cwise__, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, y_dim1, y_offset, err_bnds_norm_dim1, err_bnds_norm_offset, err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3, i__4;
real r__1, r__2;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
real dxratmax, dzratmax;
integer i__, j;
logical incr_prec__;
extern /* Subroutine */
int cla_syamv_(integer *, integer *, real *, complex *, integer *, complex *, integer *, real *, real *, integer *);
real prev_dz_z__, yk, final_dx_x__;
extern /* Subroutine */
int cla_wwaddw_(integer *, complex *, complex *, complex *);
real final_dz_z__, prevnormdx;
integer cnt;
real dyk, eps, incr_thresh__, dx_x__, dz_z__;
extern /* Subroutine */
int cla_lin_berr_(integer *, integer *, integer * , complex *, real *, real *);
real ymin;
integer y_prec_state__;
extern /* Subroutine */
int blas_csymv_x_(integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *, integer *);
integer uplo2;
extern logical lsame_(char *, char *);
extern /* Subroutine */
int blas_csymv2_x_(integer *, integer *, complex *, complex *, integer *, complex *, complex *, integer *, complex *, complex *, integer *, integer *), ccopy_(integer *, complex *, integer *, complex *, integer *);
real dxrat, dzrat;
extern /* Subroutine */
int caxpy_(integer *, complex *, complex *, integer *, complex *, integer *);
logical upper;
extern /* Subroutine */
int csymv_(char *, integer *, complex *, complex * , integer *, complex *, integer *, complex *, complex *, integer * );
real normx, normy;
extern real slamch_(char *);
extern /* Subroutine */
int xerbla_(char *, integer *);
real normdx;
extern /* Subroutine */
int csytrs_(char *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *);
real hugeval;
extern integer ilauplo_(char *);
integer x_state__, z_state__;
/* -- LAPACK computational routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Parameters .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1;
err_bnds_norm__ -= err_bnds_norm_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1;
y -= y_offset;
--berr_out__;
--res;
--ayb;
--dy;
--y_tail__;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! 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 = -13;
}
else if (*ldy < max(1,*n))
{
*info = -15;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CLA_SYRFSX_EXTENDED", &i__1);
return 0;
}
eps = slamch_("Epsilon");
hugeval = slamch_("Overflow");
/* Force HUGEVAL to Inf */
hugeval *= hugeval;
/* Using HUGEVAL may lead to spurious underflows. */
incr_thresh__ = (real) (*n) * eps;
if (lsame_(uplo, "L"))
{
uplo2 = ilauplo_("L");
}
else
{
uplo2 = ilauplo_("U");
}
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
y_prec_state__ = 1;
if (y_prec_state__ == 2)
{
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__;
y_tail__[i__3].r = 0.f;
y_tail__[i__3].i = 0.f; // , expr subst
}
}
dxrat = 0.f;
dxratmax = 0.f;
dzrat = 0.f;
dzratmax = 0.f;
final_dx_x__ = hugeval;
final_dz_z__ = hugeval;
prevnormdx = hugeval;
prev_dz_z__ = hugeval;
dz_z__ = hugeval;
dx_x__ = hugeval;
x_state__ = 1;
z_state__ = 0;
incr_prec__ = FALSE_;
i__2 = *ithresh;
for (cnt = 1;
cnt <= i__2;
++cnt)
{
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
if (y_prec_state__ == 0)
{
csymv_(uplo, n, &c_b14, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, &c_b15, &res[1], &c__1);
}
else if (y_prec_state__ == 1)
{
blas_csymv_x_(&uplo2, n, &c_b14, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, &c_b15, &res[1], &c__1, prec_type__);
}
else
{
blas_csymv2_x_(&uplo2, n, &c_b14, &a[a_offset], lda, &y[j * y_dim1 + 1], &y_tail__[1], &c__1, &c_b15, &res[1], & c__1, prec_type__);
}
/* XXX: RES is no longer needed. */
ccopy_(n, &res[1], &c__1, &dy[1], &c__1);
csytrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &dy[1], n, info);
/* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */
normx = 0.f;
normy = 0.f;
normdx = 0.f;
dz_z__ = 0.f;
ymin = hugeval;
i__3 = *n;
for (i__ = 1;
i__ <= i__3;
++i__)
{
i__4 = i__ + j * y_dim1;
yk = (r__1 = y[i__4].r, f2c_abs(r__1)) + (r__2 = r_imag(&y[i__ + j * y_dim1]), f2c_abs(r__2));
i__4 = i__;
dyk = (r__1 = dy[i__4].r, f2c_abs(r__1)) + (r__2 = r_imag(&dy[i__] ), f2c_abs(r__2));
if (yk != 0.f)
{
/* Computing MAX */
r__1 = dz_z__;
r__2 = dyk / yk; // , expr subst
dz_z__ = max(r__1,r__2);
}
else if (dyk != 0.f)
{
dz_z__ = hugeval;
}
ymin = min(ymin,yk);
normy = max(normy,yk);
if (*colequ)
{
/* Computing MAX */
r__1 = normx;
r__2 = yk * c__[i__]; // , expr subst
normx = max(r__1,r__2);
/* Computing MAX */
r__1 = normdx;
r__2 = dyk * c__[i__]; // , expr subst
normdx = max(r__1,r__2);
}
else
{
normx = normy;
normdx = max(normdx,dyk);
}
}
if (normx != 0.f)
{
dx_x__ = normdx / normx;
}
else if (normdx == 0.f)
{
dx_x__ = 0.f;
}
else
{
dx_x__ = hugeval;
}
dxrat = normdx / prevnormdx;
dzrat = dz_z__ / prev_dz_z__;
/* Check termination criteria. */
if (ymin * *rcond < incr_thresh__ * normy && y_prec_state__ < 2)
{
incr_prec__ = TRUE_;
}
if (x_state__ == 3 && dxrat <= *rthresh)
{
x_state__ = 1;
}
if (x_state__ == 1)
{
if (dx_x__ <= eps)
{
x_state__ = 2;
}
else if (dxrat > *rthresh)
{
if (y_prec_state__ != 2)
{
incr_prec__ = TRUE_;
}
else
{
x_state__ = 3;
}
}
else
{
if (dxrat > dxratmax)
{
dxratmax = dxrat;
}
}
if (x_state__ > 1)
{
final_dx_x__ = dx_x__;
}
}
if (z_state__ == 0 && dz_z__ <= *dz_ub__)
{
z_state__ = 1;
}
if (z_state__ == 3 && dzrat <= *rthresh)
{
z_state__ = 1;
}
if (z_state__ == 1)
{
if (dz_z__ <= eps)
{
z_state__ = 2;
}
else if (dz_z__ > *dz_ub__)
{
z_state__ = 0;
dzratmax = 0.f;
final_dz_z__ = hugeval;
}
else if (dzrat > *rthresh)
{
if (y_prec_state__ != 2)
{
incr_prec__ = TRUE_;
}
else
{
z_state__ = 3;
}
}
else
{
if (dzrat > dzratmax)
{
dzratmax = dzrat;
}
}
if (z_state__ > 1)
{
final_dz_z__ = dz_z__;
}
}
if (x_state__ != 1 && (*ignore_cwise__ || z_state__ != 1))
{
goto L666;
}
if (incr_prec__)
{
incr_prec__ = FALSE_;
++y_prec_state__;
i__3 = *n;
for (i__ = 1;
i__ <= i__3;
++i__)
{
i__4 = i__;
y_tail__[i__4].r = 0.f;
y_tail__[i__4].i = 0.f; // , expr subst
}
}
prevnormdx = normdx;
prev_dz_z__ = dz_z__;
/* Update soluton. */
if (y_prec_state__ < 2)
{
caxpy_(n, &c_b15, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1);
}
else
{
cla_wwaddw_(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]);
}
}
/* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't CALL F90_EXIT. */
L666: /* Set final_* when cnt hits ithresh. */
if (x_state__ == 1)
{
final_dx_x__ = dx_x__;
}
if (z_state__ == 1)
{
final_dz_z__ = dz_z__;
}
/* Compute error bounds. */
if (*n_norms__ >= 1)
{
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / ( 1 - dxratmax);
}
if (*n_norms__ >= 2)
{
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / ( 1 - dzratmax);
}
/* Compute componentwise relative backward error from formula */
/* max(i) ( f2c_abs(R(i)) / ( f2c_abs(op(A_s))*f2c_abs(Y) + f2c_abs(B_s) )(i) ) */
/* where f2c_abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. */
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
csymv_(uplo, n, &c_b14, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, &c_b15, &res[1], &c__1);
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * b_dim1;
ayb[i__] = (r__1 = b[i__3].r, f2c_abs(r__1)) + (r__2 = r_imag(&b[i__ + j * b_dim1]), f2c_abs(r__2));
}
/* Compute f2c_abs(op(A_s))*f2c_abs(Y) + f2c_abs(B_s). */
cla_syamv_(&uplo2, n, &c_b37, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, &c_b37, &ayb[1], &c__1);
cla_lin_berr_(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]);
/* End of loop for each RHS. */
}
return 0;
}
/* Subroutine */ int csyrfs_(char *uplo, integer *n, integer *nrhs, complex *
a, integer *lda, complex *af, integer *ldaf, integer *ipiv, complex *
b, integer *ldb, complex *x, integer *ldx, real *ferr, real *berr,
complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer i__, j, k;
real s, xk;
integer nz;
real eps;
integer kase;
real safe1, safe2;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
integer count;
logical upper;
extern /* Subroutine */ int csymv_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, complex *, integer *
), clacn2_(integer *, complex *, complex *, real *,
integer *, integer *);
extern doublereal slamch_(char *);
real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
real lstres;
extern /* Subroutine */ int csytrs_(char *, integer *, integer *, complex
*, integer *, integer *, complex *, integer *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CSYRFS improves the computed solution to a system of linear */
/* equations when the coefficient matrix is symmetric indefinite, and */
/* provides error bounds and backward error estimates for the solution. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* A (input) COMPLEX 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 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 CSYTRF. */
/* 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 CSYTRF. */
/* B (input) COMPLEX array, dimension (LDB,NRHS) */
/* The right hand side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (input/output) COMPLEX array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by CSYTRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* FERR (output) REAL array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) REAL array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) COMPLEX array, dimension (2*N) */
/* RWORK (workspace) REAL array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Internal Parameters */
/* =================== */
/* ITMAX is the maximum number of steps of iterative refinement. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--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;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldaf < max(1,*n)) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldx < max(1,*n)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CSYRFS", &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.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - A * X */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
q__1.r = -1.f, q__1.i = -0.f;
csymv_(uplo, n, &q__1, &a[a_offset], lda, &x[j * x_dim1 + 1], &c__1, &
c_b1, &work[1], &c__1);
/* Compute componentwise relative backward error from formula */
/* max(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. If the i-th component of the denominator is less */
/* than SAFE2, then SAFE1 is added to the i-th components of the */
/* numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
rwork[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[
i__ + j * b_dim1]), dabs(r__2));
/* L30: */
}
/* Compute abs(A)*abs(X) + abs(B). */
if (upper) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[k + j
* x_dim1]), dabs(r__2));
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + k * a_dim1;
rwork[i__] += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&a[i__ + k * a_dim1]), dabs(r__2))) * xk;
i__4 = i__ + k * a_dim1;
i__5 = i__ + j * x_dim1;
s += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 = r_imag(&a[
i__ + k * a_dim1]), dabs(r__2))) * ((r__3 = x[
i__5].r, dabs(r__3)) + (r__4 = r_imag(&x[i__ + j *
x_dim1]), dabs(r__4)));
/* L40: */
}
i__3 = k + k * a_dim1;
rwork[k] = rwork[k] + ((r__1 = a[i__3].r, dabs(r__1)) + (r__2
= r_imag(&a[k + k * a_dim1]), dabs(r__2))) * xk + s;
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[k + j
* x_dim1]), dabs(r__2));
i__3 = k + k * a_dim1;
rwork[k] += ((r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
a[k + k * a_dim1]), dabs(r__2))) * xk;
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = i__ + k * a_dim1;
rwork[i__] += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&a[i__ + k * a_dim1]), dabs(r__2))) * xk;
i__4 = i__ + k * a_dim1;
i__5 = i__ + j * x_dim1;
s += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 = r_imag(&a[
i__ + k * a_dim1]), dabs(r__2))) * ((r__3 = x[
i__5].r, dabs(r__3)) + (r__4 = r_imag(&x[i__ + j *
x_dim1]), dabs(r__4)));
/* L60: */
}
rwork[k] += s;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2))) / rwork[i__];
s = dmax(r__3,r__4);
} else {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + safe1) / (rwork[i__]
+ safe1);
s = dmax(r__3,r__4);
}
/* L80: */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if */
/* 1) The residual BERR(J) is larger than machine epsilon, and */
/* 2) BERR(J) decreased by at least a factor of 2 during the */
/* last iteration, and */
/* 3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
/* Update solution and try again. */
csytrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[1],
n, info);
caxpy_(n, &c_b1, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
lstres = berr[j];
++count;
goto L20;
}
/* Bound error from formula */
/* norm(X - XTRUE) / norm(X) .le. FERR = */
/* norm( abs(inv(A))* */
/* ( abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) / norm(X) */
/* where */
/* norm(Z) is the magnitude of the largest component of Z */
/* inv(A) is the inverse of A */
/* abs(Z) is the componentwise absolute value of the matrix or */
/* vector Z */
/* NZ is the maximum number of nonzeros in any row of A, plus 1 */
/* EPS is machine epsilon */
/* The i-th component of abs(R)+NZ*EPS*(abs(A)*abs(X)+abs(B)) */
/* is incremented by SAFE1 if the i-th component of */
/* abs(A)*abs(X) + abs(B) is less than SAFE2. */
/* Use CLACN2 to estimate the infinity-norm of the matrix */
/* inv(A) * diag(W), */
/* where W = abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__];
} else {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
clacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(A'). */
csytrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[
1], n, info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L110: */
}
} else if (kase == 2) {
/* Multiply by inv(A)*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L120: */
}
csytrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[
1], n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * x_dim1;
r__3 = lstres, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L130: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of CSYRFS */
} /* csyrfs_ */
/* Subroutine */ int clagsy_(integer *n, integer *k, real *d, complex *a,
integer *lda, integer *iseed, complex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8,
i__9;
doublereal d__1;
complex q__1, q__2, q__3, q__4;
/* Builtin functions */
double c_abs(complex *);
void c_div(complex *, complex *, complex *);
/* Local variables */
static integer i, j;
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *);
static complex alpha;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *);
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *), csymv_(char *, integer *,
complex *, complex *, integer *, complex *, integer *, complex *,
complex *, integer *);
extern real scnrm2_(integer *, complex *, integer *);
static integer ii, jj;
static complex wa, wb;
extern /* Subroutine */ int clacgv_(integer *, complex *, integer *);
static real wn;
extern /* Subroutine */ int xerbla_(char *, integer *), clarnv_(
integer *, integer *, integer *, complex *);
static complex tau;
/* -- LAPACK auxiliary test routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CLAGSY generates a complex symmetric matrix A, by pre- and post-
multiplying a real diagonal matrix D with a random unitary matrix:
A = U*D*U**T. The semi-bandwidth may then be reduced to k by
additional unitary transformations.
Arguments
=========
N (input) INTEGER
The order of the matrix A. N >= 0.
K (input) INTEGER
The number of nonzero subdiagonals within the band of A.
0 <= K <= N-1.
D (input) REAL array, dimension (N)
The diagonal elements of the diagonal matrix D.
A (output) COMPLEX array, dimension (LDA,N)
The generated n by n symmetric matrix A (the full matrix is
stored).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= N.
ISEED (input/output) INTEGER array, dimension (4)
On entry, the seed of the random number generator; the array
elements must be between 0 and 4095, and ISEED(4) must be
odd.
On exit, the seed is updated.
WORK (workspace) COMPLEX array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
Parameter adjustments */
--d;
a_dim1 = *lda;
a_offset = a_dim1 + 1;
a -= a_offset;
--iseed;
--work;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*k < 0 || *k > *n - 1) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -5;
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("CLAGSY", &i__1);
return 0;
}
/* initialize lower triangle of A to diagonal matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i = j + 1; i <= i__2; ++i) {
i__3 = i + j * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
i__1 = *n;
for (i = 1; i <= i__1; ++i) {
i__2 = i + i * a_dim1;
i__3 = i;
a[i__2].r = d[i__3], a[i__2].i = 0.f;
/* L30: */
}
/* Generate lower triangle of symmetric matrix */
for (i = *n - 1; i >= 1; --i) {
/* generate random reflection */
i__1 = *n - i + 1;
clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *n - i + 1;
wn = scnrm2_(&i__1, &work[1], &c__1);
d__1 = wn / c_abs(&work[1]);
q__1.r = d__1 * work[1].r, q__1.i = d__1 * work[1].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__1 = *n - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
d__1 = q__1.r;
tau.r = d__1, tau.i = 0.f;
}
/* apply random reflection to A(i:n,i:n) from the left
and the right
compute y := tau * A * conjg(u) */
i__1 = *n - i + 1;
clacgv_(&i__1, &work[1], &c__1);
i__1 = *n - i + 1;
csymv_("Lower", &i__1, &tau, &a[i + i * a_dim1], lda, &work[1], &c__1,
&c_b1, &work[*n + 1], &c__1);
i__1 = *n - i + 1;
clacgv_(&i__1, &work[1], &c__1);
/* compute v := y - 1/2 * tau * ( u, y ) * u */
q__3.r = -.5f, q__3.i = 0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__1 = *n - i + 1;
cdotc_(&q__4, &i__1, &work[1], &c__1, &work[*n + 1], &c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__1 = *n - i + 1;
caxpy_(&i__1, &alpha, &work[1], &c__1, &work[*n + 1], &c__1);
/* apply the transformation as a rank-2 update to A(i:n,i:n)
CALL CSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1,
$ A( I, I ), LDA ) */
i__1 = *n;
for (jj = i; jj <= i__1; ++jj) {
i__2 = *n;
for (ii = jj; ii <= i__2; ++ii) {
i__3 = ii + jj * a_dim1;
i__4 = ii + jj * a_dim1;
i__5 = ii - i + 1;
i__6 = *n + jj - i + 1;
q__3.r = work[i__5].r * work[i__6].r - work[i__5].i * work[
i__6].i, q__3.i = work[i__5].r * work[i__6].i + work[
i__5].i * work[i__6].r;
q__2.r = a[i__4].r - q__3.r, q__2.i = a[i__4].i - q__3.i;
i__7 = *n + ii - i + 1;
i__8 = jj - i + 1;
q__4.r = work[i__7].r * work[i__8].r - work[i__7].i * work[
i__8].i, q__4.i = work[i__7].r * work[i__8].i + work[
i__7].i * work[i__8].r;
q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
/* L40: */
}
/* L50: */
}
/* L60: */
}
/* Reduce number of subdiagonals to K */
i__1 = *n - 1 - *k;
for (i = 1; i <= i__1; ++i) {
/* generate reflection to annihilate A(k+i+1:n,i) */
i__2 = *n - *k - i + 1;
wn = scnrm2_(&i__2, &a[*k + i + i * a_dim1], &c__1);
d__1 = wn / c_abs(&a[*k + i + i * a_dim1]);
i__2 = *k + i + i * a_dim1;
q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = *k + i + i * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *n - *k - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[*k + i + 1 + i * a_dim1], &c__1);
i__2 = *k + i + i * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
d__1 = q__1.r;
tau.r = d__1, tau.i = 0.f;
}
/* apply reflection to A(k+i:n,i+1:k+i-1) from the left */
i__2 = *n - *k - i + 1;
i__3 = *k - 1;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*k + i + (i + 1)
* a_dim1], lda, &a[*k + i + i * a_dim1], &c__1, &c_b1, &work[
1], &c__1);
i__2 = *n - *k - i + 1;
i__3 = *k - 1;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__2, &i__3, &q__1, &a[*k + i + i * a_dim1], &c__1, &work[1],
&c__1, &a[*k + i + (i + 1) * a_dim1], lda);
/* apply reflection to A(k+i:n,k+i:n) from the left and the rig
ht
compute y := tau * A * conjg(u) */
i__2 = *n - *k - i + 1;
clacgv_(&i__2, &a[*k + i + i * a_dim1], &c__1);
i__2 = *n - *k - i + 1;
csymv_("Lower", &i__2, &tau, &a[*k + i + (*k + i) * a_dim1], lda, &a[*
k + i + i * a_dim1], &c__1, &c_b1, &work[1], &c__1);
i__2 = *n - *k - i + 1;
clacgv_(&i__2, &a[*k + i + i * a_dim1], &c__1);
/* compute v := y - 1/2 * tau * ( u, y ) * u */
q__3.r = -.5f, q__3.i = 0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__2 = *n - *k - i + 1;
cdotc_(&q__4, &i__2, &a[*k + i + i * a_dim1], &c__1, &work[1], &c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__2 = *n - *k - i + 1;
caxpy_(&i__2, &alpha, &a[*k + i + i * a_dim1], &c__1, &work[1], &c__1)
;
/* apply symmetric rank-2 update to A(k+i:n,k+i:n)
CALL CSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1,
$ A( K+I, K+I ), LDA ) */
i__2 = *n;
for (jj = *k + i; jj <= i__2; ++jj) {
i__3 = *n;
for (ii = jj; ii <= i__3; ++ii) {
i__4 = ii + jj * a_dim1;
i__5 = ii + jj * a_dim1;
i__6 = ii + i * a_dim1;
i__7 = jj - *k - i + 1;
q__3.r = a[i__6].r * work[i__7].r - a[i__6].i * work[i__7].i,
q__3.i = a[i__6].r * work[i__7].i + a[i__6].i * work[
i__7].r;
q__2.r = a[i__5].r - q__3.r, q__2.i = a[i__5].i - q__3.i;
i__8 = ii - *k - i + 1;
i__9 = jj + i * a_dim1;
q__4.r = work[i__8].r * a[i__9].r - work[i__8].i * a[i__9].i,
q__4.i = work[i__8].r * a[i__9].i + work[i__8].i * a[
i__9].r;
q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i;
a[i__4].r = q__1.r, a[i__4].i = q__1.i;
/* L70: */
}
/* L80: */
}
i__2 = *k + i + i * a_dim1;
q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
i__2 = *n;
for (j = *k + i + 1; j <= i__2; ++j) {
i__3 = j + i * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L90: */
}
/* L100: */
}
/* Store full symmetric matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i = j + 1; i <= i__2; ++i) {
i__3 = j + i * a_dim1;
i__4 = i + j * a_dim1;
a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;
/* L110: */
}
/* L120: */
}
return 0;
/* End of CLAGSY */
} /* clagsy_ */
/* Subroutine */ int clagsy_(integer *n, integer *k, real *d__, complex *a,
integer *lda, integer *iseed, complex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8,
i__9;
real r__1;
complex q__1, q__2, q__3, q__4;
/* Local variables */
integer i__, j, ii, jj;
complex wa, wb;
real wn;
complex tau;
complex alpha;
/* -- LAPACK auxiliary test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLAGSY generates a complex symmetric matrix A, by pre- and post- */
/* multiplying a real diagonal matrix D with a random unitary matrix: */
/* A = U*D*U**T. The semi-bandwidth may then be reduced to k by */
/* additional unitary transformations. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* K (input) INTEGER */
/* The number of nonzero subdiagonals within the band of A. */
/* 0 <= K <= N-1. */
/* D (input) REAL array, dimension (N) */
/* The diagonal elements of the diagonal matrix D. */
/* A (output) COMPLEX array, dimension (LDA,N) */
/* The generated n by n symmetric matrix A (the full matrix is */
/* stored). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= N. */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry, the seed of the random number generator; the array */
/* elements must be between 0 and 4095, and ISEED(4) must be */
/* odd. */
/* On exit, the seed is updated. */
/* WORK (workspace) COMPLEX array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
--d__;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--iseed;
--work;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*k < 0 || *k > *n - 1) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -5;
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("CLAGSY", &i__1);
return 0;
}
/* initialize lower triangle of A to diagonal matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * a_dim1;
i__3 = i__;
a[i__2].r = d__[i__3], a[i__2].i = 0.f;
/* L30: */
}
/* Generate lower triangle of symmetric matrix */
for (i__ = *n - 1; i__ >= 1; --i__) {
/* generate random reflection */
i__1 = *n - i__ + 1;
clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *n - i__ + 1;
wn = scnrm2_(&i__1, &work[1], &c__1);
r__1 = wn / c_abs(&work[1]);
q__1.r = r__1 * work[1].r, q__1.i = r__1 * work[1].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__1 = *n - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* apply random reflection to A(i:n,i:n) from the left */
/* and the right */
/* compute y := tau * A * conjg(u) */
i__1 = *n - i__ + 1;
clacgv_(&i__1, &work[1], &c__1);
i__1 = *n - i__ + 1;
csymv_("Lower", &i__1, &tau, &a[i__ + i__ * a_dim1], lda, &work[1], &
c__1, &c_b1, &work[*n + 1], &c__1);
i__1 = *n - i__ + 1;
clacgv_(&i__1, &work[1], &c__1);
/* compute v := y - 1/2 * tau * ( u, y ) * u */
q__3.r = -.5f, q__3.i = -0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__1 = *n - i__ + 1;
cdotc_(&q__4, &i__1, &work[1], &c__1, &work[*n + 1], &c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__1 = *n - i__ + 1;
caxpy_(&i__1, &alpha, &work[1], &c__1, &work[*n + 1], &c__1);
/* apply the transformation as a rank-2 update to A(i:n,i:n) */
/* CALL CSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1, */
/* $ A( I, I ), LDA ) */
i__1 = *n;
for (jj = i__; jj <= i__1; ++jj) {
i__2 = *n;
for (ii = jj; ii <= i__2; ++ii) {
i__3 = ii + jj * a_dim1;
i__4 = ii + jj * a_dim1;
i__5 = ii - i__ + 1;
i__6 = *n + jj - i__ + 1;
q__3.r = work[i__5].r * work[i__6].r - work[i__5].i * work[
i__6].i, q__3.i = work[i__5].r * work[i__6].i + work[
i__5].i * work[i__6].r;
q__2.r = a[i__4].r - q__3.r, q__2.i = a[i__4].i - q__3.i;
i__7 = *n + ii - i__ + 1;
i__8 = jj - i__ + 1;
q__4.r = work[i__7].r * work[i__8].r - work[i__7].i * work[
i__8].i, q__4.i = work[i__7].r * work[i__8].i + work[
i__7].i * work[i__8].r;
q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
/* L40: */
}
/* L50: */
}
/* L60: */
}
/* Reduce number of subdiagonals to K */
i__1 = *n - 1 - *k;
for (i__ = 1; i__ <= i__1; ++i__) {
/* generate reflection to annihilate A(k+i+1:n,i) */
i__2 = *n - *k - i__ + 1;
wn = scnrm2_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
r__1 = wn / c_abs(&a[*k + i__ + i__ * a_dim1]);
i__2 = *k + i__ + i__ * a_dim1;
q__1.r = r__1 * a[i__2].r, q__1.i = r__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = *k + i__ + i__ * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *n - *k - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[*k + i__ + 1 + i__ * a_dim1], &c__1);
i__2 = *k + i__ + i__ * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* apply reflection to A(k+i:n,i+1:k+i-1) from the left */
i__2 = *n - *k - i__ + 1;
i__3 = *k - 1;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*k + i__ + (i__
+ 1) * a_dim1], lda, &a[*k + i__ + i__ * a_dim1], &c__1, &
c_b1, &work[1], &c__1);
i__2 = *n - *k - i__ + 1;
i__3 = *k - 1;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&i__2, &i__3, &q__1, &a[*k + i__ + i__ * a_dim1], &c__1, &work[
1], &c__1, &a[*k + i__ + (i__ + 1) * a_dim1], lda);
/* apply reflection to A(k+i:n,k+i:n) from the left and the right */
/* compute y := tau * A * conjg(u) */
i__2 = *n - *k - i__ + 1;
clacgv_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
i__2 = *n - *k - i__ + 1;
csymv_("Lower", &i__2, &tau, &a[*k + i__ + (*k + i__) * a_dim1], lda,
&a[*k + i__ + i__ * a_dim1], &c__1, &c_b1, &work[1], &c__1);
i__2 = *n - *k - i__ + 1;
clacgv_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
/* compute v := y - 1/2 * tau * ( u, y ) * u */
q__3.r = -.5f, q__3.i = -0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__2 = *n - *k - i__ + 1;
cdotc_(&q__4, &i__2, &a[*k + i__ + i__ * a_dim1], &c__1, &work[1], &
c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__2 = *n - *k - i__ + 1;
caxpy_(&i__2, &alpha, &a[*k + i__ + i__ * a_dim1], &c__1, &work[1], &
c__1);
/* apply symmetric rank-2 update to A(k+i:n,k+i:n) */
/* CALL CSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1, */
/* $ A( K+I, K+I ), LDA ) */
i__2 = *n;
for (jj = *k + i__; jj <= i__2; ++jj) {
i__3 = *n;
for (ii = jj; ii <= i__3; ++ii) {
i__4 = ii + jj * a_dim1;
i__5 = ii + jj * a_dim1;
i__6 = ii + i__ * a_dim1;
i__7 = jj - *k - i__ + 1;
q__3.r = a[i__6].r * work[i__7].r - a[i__6].i * work[i__7].i,
q__3.i = a[i__6].r * work[i__7].i + a[i__6].i * work[
i__7].r;
q__2.r = a[i__5].r - q__3.r, q__2.i = a[i__5].i - q__3.i;
i__8 = ii - *k - i__ + 1;
i__9 = jj + i__ * a_dim1;
q__4.r = work[i__8].r * a[i__9].r - work[i__8].i * a[i__9].i,
q__4.i = work[i__8].r * a[i__9].i + work[i__8].i * a[
i__9].r;
q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i;
a[i__4].r = q__1.r, a[i__4].i = q__1.i;
/* L70: */
}
/* L80: */
}
i__2 = *k + i__ + i__ * a_dim1;
q__1.r = -wa.r, q__1.i = -wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
i__2 = *n;
for (j = *k + i__ + 1; j <= i__2; ++j) {
i__3 = j + i__ * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L90: */
}
/* L100: */
}
/* Store full symmetric matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = j + i__ * a_dim1;
i__4 = i__ + j * a_dim1;
a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;
/* L110: */
}
/* L120: */
}
return 0;
/* End of CLAGSY */
} /* clagsy_ */
/* Subroutine */ int csytri_(char *uplo, integer *n, complex *a, integer *lda,
integer *ipiv, complex *work, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CSYTRI computes the inverse of a complex symmetric indefinite matrix
A using the factorization A = U*D*U**T or A = L*D*L**T computed by
CSYTRF.
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.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by CSYTRF.
On exit, if INFO = 0, the (symmetric) inverse of the original
matrix. If UPLO = 'U', the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = 'L' the lower triangular part of the
inverse is formed and the part of A above the diagonal is
not referenced.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CSYTRF.
WORK (workspace) COMPLEX array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
inverse could not be computed.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static complex c_b1 = {1.f,0.f};
static complex c_b2 = {0.f,0.f};
static integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
complex q__1, q__2, q__3;
/* Builtin functions */
void c_div(complex *, complex *, complex *);
/* Local variables */
static complex temp, akkp1, d__;
static integer k;
static complex t;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *);
extern /* Complex */ VOID cdotu_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern /* Subroutine */ int cswap_(integer *, complex *, integer *,
complex *, integer *);
static integer kstep;
static logical upper;
extern /* Subroutine */ int csymv_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, complex *, integer *
);
static complex ak;
static integer kp;
extern /* Subroutine */ int xerbla_(char *, integer *);
static complex akp1;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--ipiv;
--work;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CSYTRI", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Check that the diagonal matrix D is nonsingular. */
if (upper) {
/* Upper triangular storage: examine D from bottom to top */
for (*info = *n; *info >= 1; --(*info)) {
i__1 = a_subscr(*info, *info);
if (ipiv[*info] > 0 && (a[i__1].r == 0.f && a[i__1].i == 0.f)) {
return 0;
}
/* L10: */
}
} else {
/* Lower triangular storage: examine D from top to bottom. */
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
i__2 = a_subscr(*info, *info);
if (ipiv[*info] > 0 && (a[i__2].r == 0.f && a[i__2].i == 0.f)) {
return 0;
}
/* L20: */
}
}
*info = 0;
if (upper) {
/* Compute inv(A) from the factorization A = U*D*U'.
K is the main loop index, increasing from 1 to N in steps of
1 or 2, depending on the size of the diagonal blocks. */
k = 1;
L30:
/* If K > N, exit from loop. */
if (k > *n) {
goto L40;
}
if (ipiv[k] > 0) {
/* 1 x 1 diagonal block
Invert the diagonal block. */
i__1 = a_subscr(k, k);
c_div(&q__1, &c_b1, &a_ref(k, k));
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
/* Compute column K of the inverse. */
if (k > 1) {
i__1 = k - 1;
ccopy_(&i__1, &a_ref(1, k), &c__1, &work[1], &c__1);
i__1 = k - 1;
q__1.r = -1.f, q__1.i = 0.f;
csymv_(uplo, &i__1, &q__1, &a[a_offset], lda, &work[1], &c__1,
&c_b2, &a_ref(1, k), &c__1);
i__1 = a_subscr(k, k);
i__2 = a_subscr(k, k);
i__3 = k - 1;
cdotu_(&q__2, &i__3, &work[1], &c__1, &a_ref(1, k), &c__1);
q__1.r = a[i__2].r - q__2.r, q__1.i = a[i__2].i - q__2.i;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
}
kstep = 1;
} else {
/* 2 x 2 diagonal block
Invert the diagonal block. */
i__1 = a_subscr(k, k + 1);
t.r = a[i__1].r, t.i = a[i__1].i;
c_div(&q__1, &a_ref(k, k), &t);
ak.r = q__1.r, ak.i = q__1.i;
c_div(&q__1, &a_ref(k + 1, k + 1), &t);
akp1.r = q__1.r, akp1.i = q__1.i;
c_div(&q__1, &a_ref(k, k + 1), &t);
akkp1.r = q__1.r, akkp1.i = q__1.i;
q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r * akp1.i +
ak.i * akp1.r;
q__2.r = q__3.r - 1.f, q__2.i = q__3.i + 0.f;
q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i
* q__2.r;
d__.r = q__1.r, d__.i = q__1.i;
i__1 = a_subscr(k, k);
c_div(&q__1, &akp1, &d__);
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = a_subscr(k + 1, k + 1);
c_div(&q__1, &ak, &d__);
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = a_subscr(k, k + 1);
q__2.r = -akkp1.r, q__2.i = -akkp1.i;
c_div(&q__1, &q__2, &d__);
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
/* Compute columns K and K+1 of the inverse. */
if (k > 1) {
i__1 = k - 1;
ccopy_(&i__1, &a_ref(1, k), &c__1, &work[1], &c__1);
i__1 = k - 1;
q__1.r = -1.f, q__1.i = 0.f;
csymv_(uplo, &i__1, &q__1, &a[a_offset], lda, &work[1], &c__1,
&c_b2, &a_ref(1, k), &c__1);
i__1 = a_subscr(k, k);
i__2 = a_subscr(k, k);
i__3 = k - 1;
cdotu_(&q__2, &i__3, &work[1], &c__1, &a_ref(1, k), &c__1);
q__1.r = a[i__2].r - q__2.r, q__1.i = a[i__2].i - q__2.i;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = a_subscr(k, k + 1);
i__2 = a_subscr(k, k + 1);
i__3 = k - 1;
cdotu_(&q__2, &i__3, &a_ref(1, k), &c__1, &a_ref(1, k + 1), &
c__1);
q__1.r = a[i__2].r - q__2.r, q__1.i = a[i__2].i - q__2.i;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = k - 1;
ccopy_(&i__1, &a_ref(1, k + 1), &c__1, &work[1], &c__1);
i__1 = k - 1;
q__1.r = -1.f, q__1.i = 0.f;
csymv_(uplo, &i__1, &q__1, &a[a_offset], lda, &work[1], &c__1,
&c_b2, &a_ref(1, k + 1), &c__1);
i__1 = a_subscr(k + 1, k + 1);
i__2 = a_subscr(k + 1, k + 1);
i__3 = k - 1;
cdotu_(&q__2, &i__3, &work[1], &c__1, &a_ref(1, k + 1), &c__1)
;
q__1.r = a[i__2].r - q__2.r, q__1.i = a[i__2].i - q__2.i;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
}
kstep = 2;
}
kp = (i__1 = ipiv[k], abs(i__1));
if (kp != k) {
/* Interchange rows and columns K and KP in the leading
submatrix A(1:k+1,1:k+1) */
i__1 = kp - 1;
cswap_(&i__1, &a_ref(1, k), &c__1, &a_ref(1, kp), &c__1);
i__1 = k - kp - 1;
cswap_(&i__1, &a_ref(kp + 1, k), &c__1, &a_ref(kp, kp + 1), lda);
i__1 = a_subscr(k, k);
temp.r = a[i__1].r, temp.i = a[i__1].i;
i__1 = a_subscr(k, k);
i__2 = a_subscr(kp, kp);
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = a_subscr(kp, kp);
a[i__1].r = temp.r, a[i__1].i = temp.i;
if (kstep == 2) {
i__1 = a_subscr(k, k + 1);
temp.r = a[i__1].r, temp.i = a[i__1].i;
i__1 = a_subscr(k, k + 1);
i__2 = a_subscr(kp, k + 1);
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = a_subscr(kp, k + 1);
a[i__1].r = temp.r, a[i__1].i = temp.i;
}
}
k += kstep;
goto L30;
L40:
;
} else {
/* Compute inv(A) from the factorization A = L*D*L'.
K is the main loop index, increasing from 1 to N in steps of
1 or 2, depending on the size of the diagonal blocks. */
k = *n;
L50:
/* If K < 1, exit from loop. */
if (k < 1) {
goto L60;
}
if (ipiv[k] > 0) {
/* 1 x 1 diagonal block
Invert the diagonal block. */
i__1 = a_subscr(k, k);
c_div(&q__1, &c_b1, &a_ref(k, k));
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
/* Compute column K of the inverse. */
if (k < *n) {
i__1 = *n - k;
ccopy_(&i__1, &a_ref(k + 1, k), &c__1, &work[1], &c__1);
i__1 = *n - k;
q__1.r = -1.f, q__1.i = 0.f;
csymv_(uplo, &i__1, &q__1, &a_ref(k + 1, k + 1), lda, &work[1]
, &c__1, &c_b2, &a_ref(k + 1, k), &c__1);
i__1 = a_subscr(k, k);
i__2 = a_subscr(k, k);
i__3 = *n - k;
cdotu_(&q__2, &i__3, &work[1], &c__1, &a_ref(k + 1, k), &c__1)
;
q__1.r = a[i__2].r - q__2.r, q__1.i = a[i__2].i - q__2.i;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
}
kstep = 1;
} else {
/* 2 x 2 diagonal block
Invert the diagonal block. */
i__1 = a_subscr(k, k - 1);
t.r = a[i__1].r, t.i = a[i__1].i;
c_div(&q__1, &a_ref(k - 1, k - 1), &t);
ak.r = q__1.r, ak.i = q__1.i;
c_div(&q__1, &a_ref(k, k), &t);
akp1.r = q__1.r, akp1.i = q__1.i;
c_div(&q__1, &a_ref(k, k - 1), &t);
akkp1.r = q__1.r, akkp1.i = q__1.i;
q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r * akp1.i +
ak.i * akp1.r;
q__2.r = q__3.r - 1.f, q__2.i = q__3.i + 0.f;
q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i
* q__2.r;
d__.r = q__1.r, d__.i = q__1.i;
i__1 = a_subscr(k - 1, k - 1);
c_div(&q__1, &akp1, &d__);
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = a_subscr(k, k);
c_div(&q__1, &ak, &d__);
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = a_subscr(k, k - 1);
q__2.r = -akkp1.r, q__2.i = -akkp1.i;
c_div(&q__1, &q__2, &d__);
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
/* Compute columns K-1 and K of the inverse. */
if (k < *n) {
i__1 = *n - k;
ccopy_(&i__1, &a_ref(k + 1, k), &c__1, &work[1], &c__1);
i__1 = *n - k;
q__1.r = -1.f, q__1.i = 0.f;
csymv_(uplo, &i__1, &q__1, &a_ref(k + 1, k + 1), lda, &work[1]
, &c__1, &c_b2, &a_ref(k + 1, k), &c__1);
i__1 = a_subscr(k, k);
i__2 = a_subscr(k, k);
i__3 = *n - k;
cdotu_(&q__2, &i__3, &work[1], &c__1, &a_ref(k + 1, k), &c__1)
;
q__1.r = a[i__2].r - q__2.r, q__1.i = a[i__2].i - q__2.i;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = a_subscr(k, k - 1);
i__2 = a_subscr(k, k - 1);
i__3 = *n - k;
cdotu_(&q__2, &i__3, &a_ref(k + 1, k), &c__1, &a_ref(k + 1, k
- 1), &c__1);
q__1.r = a[i__2].r - q__2.r, q__1.i = a[i__2].i - q__2.i;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = *n - k;
ccopy_(&i__1, &a_ref(k + 1, k - 1), &c__1, &work[1], &c__1);
i__1 = *n - k;
q__1.r = -1.f, q__1.i = 0.f;
csymv_(uplo, &i__1, &q__1, &a_ref(k + 1, k + 1), lda, &work[1]
, &c__1, &c_b2, &a_ref(k + 1, k - 1), &c__1);
i__1 = a_subscr(k - 1, k - 1);
i__2 = a_subscr(k - 1, k - 1);
i__3 = *n - k;
cdotu_(&q__2, &i__3, &work[1], &c__1, &a_ref(k + 1, k - 1), &
c__1);
q__1.r = a[i__2].r - q__2.r, q__1.i = a[i__2].i - q__2.i;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
}
kstep = 2;
}
kp = (i__1 = ipiv[k], abs(i__1));
if (kp != k) {
/* Interchange rows and columns K and KP in the trailing
submatrix A(k-1:n,k-1:n) */
if (kp < *n) {
i__1 = *n - kp;
cswap_(&i__1, &a_ref(kp + 1, k), &c__1, &a_ref(kp + 1, kp), &
c__1);
}
i__1 = kp - k - 1;
cswap_(&i__1, &a_ref(k + 1, k), &c__1, &a_ref(kp, k + 1), lda);
i__1 = a_subscr(k, k);
temp.r = a[i__1].r, temp.i = a[i__1].i;
i__1 = a_subscr(k, k);
i__2 = a_subscr(kp, kp);
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = a_subscr(kp, kp);
a[i__1].r = temp.r, a[i__1].i = temp.i;
if (kstep == 2) {
i__1 = a_subscr(k, k - 1);
temp.r = a[i__1].r, temp.i = a[i__1].i;
i__1 = a_subscr(k, k - 1);
i__2 = a_subscr(kp, k - 1);
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = a_subscr(kp, k - 1);
a[i__1].r = temp.r, a[i__1].i = temp.i;
}
}
k -= kstep;
goto L50;
L60:
;
}
return 0;
/* End of CSYTRI */
} /* csytri_ */
/* Subroutine */
int csytri_rook_(char *uplo, integer *n, complex *a, integer *lda, integer *ipiv, complex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
complex q__1, q__2, q__3;
/* Builtin functions */
void c_div(complex *, complex *, complex *);
/* Local variables */
complex d__;
integer k;
complex t, ak;
integer kp;
complex akp1, temp, akkp1;
extern logical lsame_(char *, char *);
extern /* Subroutine */
int ccopy_(integer *, complex *, integer *, complex *, integer *);
extern /* Complex */
VOID cdotu_f2c_(complex *, integer *, complex *, integer *, complex *, integer *);
extern /* Subroutine */
int cswap_(integer *, complex *, integer *, complex *, integer *);
integer kstep;
logical upper;
extern /* Subroutine */
int csymv_(char *, integer *, complex *, complex * , integer *, complex *, integer *, complex *, complex *, integer * ), xerbla_(char *, 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 .. */
/* .. */
/* .. 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;
--ipiv;
--work;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L"))
{
*info = -1;
}
else if (*n < 0)
{
*info = -2;
}
else if (*lda < max(1,*n))
{
*info = -4;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CSYTRI_ROOK", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0)
{
return 0;
}
/* Check that the diagonal matrix D is nonsingular. */
if (upper)
{
/* Upper triangular storage: examine D from bottom to top */
for (*info = *n;
*info >= 1;
--(*info))
{
i__1 = *info + *info * a_dim1;
if (ipiv[*info] > 0 && (a[i__1].r == 0.f && a[i__1].i == 0.f))
{
return 0;
}
/* L10: */
}
}
else
{
/* Lower triangular storage: examine D from top to bottom. */
i__1 = *n;
for (*info = 1;
*info <= i__1;
++(*info))
{
i__2 = *info + *info * a_dim1;
if (ipiv[*info] > 0 && (a[i__2].r == 0.f && a[i__2].i == 0.f))
{
return 0;
}
/* L20: */
}
}
*info = 0;
if (upper)
{
/* Compute inv(A) from the factorization A = U*D*U**T. */
/* K is the main loop index, increasing from 1 to N in steps of */
/* 1 or 2, depending on the size of the diagonal blocks. */
k = 1;
L30: /* If K > N, exit from loop. */
if (k > *n)
{
goto L40;
}
if (ipiv[k] > 0)
{
/* 1 x 1 diagonal block */
/* Invert the diagonal block. */
i__1 = k + k * a_dim1;
c_div(&q__1, &c_b1, &a[k + k * a_dim1]);
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
/* Compute column K of the inverse. */
if (k > 1)
{
i__1 = k - 1;
ccopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &work[1], &c__1);
i__1 = k - 1;
q__1.r = -1.f;
q__1.i = -0.f; // , expr subst
csymv_(uplo, &i__1, &q__1, &a[a_offset], lda, &work[1], &c__1, &c_b2, &a[k * a_dim1 + 1], &c__1);
i__1 = k + k * a_dim1;
i__2 = k + k * a_dim1;
i__3 = k - 1;
cdotu_f2c_(&q__2, &i__3, &work[1], &c__1, &a[k * a_dim1 + 1], & c__1);
q__1.r = a[i__2].r - q__2.r;
q__1.i = a[i__2].i - q__2.i; // , expr subst
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
}
kstep = 1;
}
else
{
/* 2 x 2 diagonal block */
/* Invert the diagonal block. */
i__1 = k + (k + 1) * a_dim1;
t.r = a[i__1].r;
t.i = a[i__1].i; // , expr subst
c_div(&q__1, &a[k + k * a_dim1], &t);
ak.r = q__1.r;
ak.i = q__1.i; // , expr subst
c_div(&q__1, &a[k + 1 + (k + 1) * a_dim1], &t);
akp1.r = q__1.r;
akp1.i = q__1.i; // , expr subst
c_div(&q__1, &a[k + (k + 1) * a_dim1], &t);
akkp1.r = q__1.r;
akkp1.i = q__1.i; // , expr subst
q__3.r = ak.r * akp1.r - ak.i * akp1.i;
q__3.i = ak.r * akp1.i + ak.i * akp1.r; // , expr subst
q__2.r = q__3.r - 1.f;
q__2.i = q__3.i - 0.f; // , expr subst
q__1.r = t.r * q__2.r - t.i * q__2.i;
q__1.i = t.r * q__2.i + t.i * q__2.r; // , expr subst
d__.r = q__1.r;
d__.i = q__1.i; // , expr subst
i__1 = k + k * a_dim1;
c_div(&q__1, &akp1, &d__);
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
i__1 = k + 1 + (k + 1) * a_dim1;
c_div(&q__1, &ak, &d__);
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
i__1 = k + (k + 1) * a_dim1;
q__2.r = -akkp1.r;
q__2.i = -akkp1.i; // , expr subst
c_div(&q__1, &q__2, &d__);
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
/* Compute columns K and K+1 of the inverse. */
if (k > 1)
{
i__1 = k - 1;
ccopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &work[1], &c__1);
i__1 = k - 1;
q__1.r = -1.f;
q__1.i = -0.f; // , expr subst
csymv_(uplo, &i__1, &q__1, &a[a_offset], lda, &work[1], &c__1, &c_b2, &a[k * a_dim1 + 1], &c__1);
i__1 = k + k * a_dim1;
i__2 = k + k * a_dim1;
i__3 = k - 1;
cdotu_f2c_(&q__2, &i__3, &work[1], &c__1, &a[k * a_dim1 + 1], & c__1);
q__1.r = a[i__2].r - q__2.r;
q__1.i = a[i__2].i - q__2.i; // , expr subst
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
i__1 = k + (k + 1) * a_dim1;
i__2 = k + (k + 1) * a_dim1;
i__3 = k - 1;
cdotu_f2c_(&q__2, &i__3, &a[k * a_dim1 + 1], &c__1, &a[(k + 1) * a_dim1 + 1], &c__1);
q__1.r = a[i__2].r - q__2.r;
q__1.i = a[i__2].i - q__2.i; // , expr subst
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
i__1 = k - 1;
ccopy_(&i__1, &a[(k + 1) * a_dim1 + 1], &c__1, &work[1], & c__1);
i__1 = k - 1;
q__1.r = -1.f;
q__1.i = -0.f; // , expr subst
csymv_(uplo, &i__1, &q__1, &a[a_offset], lda, &work[1], &c__1, &c_b2, &a[(k + 1) * a_dim1 + 1], &c__1);
i__1 = k + 1 + (k + 1) * a_dim1;
i__2 = k + 1 + (k + 1) * a_dim1;
i__3 = k - 1;
cdotu_f2c_(&q__2, &i__3, &work[1], &c__1, &a[(k + 1) * a_dim1 + 1] , &c__1);
q__1.r = a[i__2].r - q__2.r;
q__1.i = a[i__2].i - q__2.i; // , expr subst
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
}
kstep = 2;
}
if (kstep == 1)
{
/* Interchange rows and columns K and IPIV(K) in the leading */
/* submatrix A(1:k+1,1:k+1) */
kp = ipiv[k];
if (kp != k)
{
if (kp > 1)
{
i__1 = kp - 1;
cswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &c__1);
}
i__1 = k - kp - 1;
cswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + (kp + 1) * a_dim1], lda);
i__1 = k + k * a_dim1;
temp.r = a[i__1].r;
temp.i = a[i__1].i; // , expr subst
i__1 = k + k * a_dim1;
i__2 = kp + kp * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = kp + kp * a_dim1;
a[i__1].r = temp.r;
a[i__1].i = temp.i; // , expr subst
}
}
else
{
/* Interchange rows and columns K and K+1 with -IPIV(K) and */
/* -IPIV(K+1)in the leading submatrix A(1:k+1,1:k+1) */
kp = -ipiv[k];
if (kp != k)
{
if (kp > 1)
{
i__1 = kp - 1;
cswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &c__1);
}
i__1 = k - kp - 1;
cswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + (kp + 1) * a_dim1], lda);
i__1 = k + k * a_dim1;
temp.r = a[i__1].r;
temp.i = a[i__1].i; // , expr subst
i__1 = k + k * a_dim1;
i__2 = kp + kp * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = kp + kp * a_dim1;
a[i__1].r = temp.r;
a[i__1].i = temp.i; // , expr subst
i__1 = k + (k + 1) * a_dim1;
temp.r = a[i__1].r;
temp.i = a[i__1].i; // , expr subst
i__1 = k + (k + 1) * a_dim1;
i__2 = kp + (k + 1) * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = kp + (k + 1) * a_dim1;
a[i__1].r = temp.r;
a[i__1].i = temp.i; // , expr subst
}
++k;
kp = -ipiv[k];
if (kp != k)
{
if (kp > 1)
{
i__1 = kp - 1;
cswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &c__1);
}
i__1 = k - kp - 1;
cswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + (kp + 1) * a_dim1], lda);
i__1 = k + k * a_dim1;
temp.r = a[i__1].r;
temp.i = a[i__1].i; // , expr subst
i__1 = k + k * a_dim1;
i__2 = kp + kp * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = kp + kp * a_dim1;
a[i__1].r = temp.r;
a[i__1].i = temp.i; // , expr subst
}
}
++k;
goto L30;
L40:
;
}
else
{
/* Compute inv(A) from the factorization A = L*D*L**T. */
/* K is the main loop index, increasing from 1 to N in steps of */
/* 1 or 2, depending on the size of the diagonal blocks. */
k = *n;
L50: /* If K < 1, exit from loop. */
if (k < 1)
{
goto L60;
}
if (ipiv[k] > 0)
{
/* 1 x 1 diagonal block */
/* Invert the diagonal block. */
i__1 = k + k * a_dim1;
c_div(&q__1, &c_b1, &a[k + k * a_dim1]);
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
/* Compute column K of the inverse. */
if (k < *n)
{
i__1 = *n - k;
ccopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &work[1], &c__1);
i__1 = *n - k;
q__1.r = -1.f;
q__1.i = -0.f; // , expr subst
csymv_(uplo, &i__1, &q__1, &a[k + 1 + (k + 1) * a_dim1], lda, &work[1], &c__1, &c_b2, &a[k + 1 + k * a_dim1], &c__1);
i__1 = k + k * a_dim1;
i__2 = k + k * a_dim1;
i__3 = *n - k;
cdotu_f2c_(&q__2, &i__3, &work[1], &c__1, &a[k + 1 + k * a_dim1], &c__1);
q__1.r = a[i__2].r - q__2.r;
q__1.i = a[i__2].i - q__2.i; // , expr subst
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
}
kstep = 1;
}
else
{
/* 2 x 2 diagonal block */
/* Invert the diagonal block. */
i__1 = k + (k - 1) * a_dim1;
t.r = a[i__1].r;
t.i = a[i__1].i; // , expr subst
c_div(&q__1, &a[k - 1 + (k - 1) * a_dim1], &t);
ak.r = q__1.r;
ak.i = q__1.i; // , expr subst
c_div(&q__1, &a[k + k * a_dim1], &t);
akp1.r = q__1.r;
akp1.i = q__1.i; // , expr subst
c_div(&q__1, &a[k + (k - 1) * a_dim1], &t);
akkp1.r = q__1.r;
akkp1.i = q__1.i; // , expr subst
q__3.r = ak.r * akp1.r - ak.i * akp1.i;
q__3.i = ak.r * akp1.i + ak.i * akp1.r; // , expr subst
q__2.r = q__3.r - 1.f;
q__2.i = q__3.i - 0.f; // , expr subst
q__1.r = t.r * q__2.r - t.i * q__2.i;
q__1.i = t.r * q__2.i + t.i * q__2.r; // , expr subst
d__.r = q__1.r;
d__.i = q__1.i; // , expr subst
i__1 = k - 1 + (k - 1) * a_dim1;
c_div(&q__1, &akp1, &d__);
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
i__1 = k + k * a_dim1;
c_div(&q__1, &ak, &d__);
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
i__1 = k + (k - 1) * a_dim1;
q__2.r = -akkp1.r;
q__2.i = -akkp1.i; // , expr subst
c_div(&q__1, &q__2, &d__);
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
/* Compute columns K-1 and K of the inverse. */
if (k < *n)
{
i__1 = *n - k;
ccopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &work[1], &c__1);
i__1 = *n - k;
q__1.r = -1.f;
q__1.i = -0.f; // , expr subst
csymv_(uplo, &i__1, &q__1, &a[k + 1 + (k + 1) * a_dim1], lda, &work[1], &c__1, &c_b2, &a[k + 1 + k * a_dim1], &c__1);
i__1 = k + k * a_dim1;
i__2 = k + k * a_dim1;
i__3 = *n - k;
cdotu_f2c_(&q__2, &i__3, &work[1], &c__1, &a[k + 1 + k * a_dim1], &c__1);
q__1.r = a[i__2].r - q__2.r;
q__1.i = a[i__2].i - q__2.i; // , expr subst
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
i__1 = k + (k - 1) * a_dim1;
i__2 = k + (k - 1) * a_dim1;
i__3 = *n - k;
cdotu_f2c_(&q__2, &i__3, &a[k + 1 + k * a_dim1], &c__1, &a[k + 1 + (k - 1) * a_dim1], &c__1);
q__1.r = a[i__2].r - q__2.r;
q__1.i = a[i__2].i - q__2.i; // , expr subst
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
i__1 = *n - k;
ccopy_(&i__1, &a[k + 1 + (k - 1) * a_dim1], &c__1, &work[1], & c__1);
i__1 = *n - k;
q__1.r = -1.f;
q__1.i = -0.f; // , expr subst
csymv_(uplo, &i__1, &q__1, &a[k + 1 + (k + 1) * a_dim1], lda, &work[1], &c__1, &c_b2, &a[k + 1 + (k - 1) * a_dim1], &c__1);
i__1 = k - 1 + (k - 1) * a_dim1;
i__2 = k - 1 + (k - 1) * a_dim1;
i__3 = *n - k;
cdotu_f2c_(&q__2, &i__3, &work[1], &c__1, &a[k + 1 + (k - 1) * a_dim1], &c__1);
q__1.r = a[i__2].r - q__2.r;
q__1.i = a[i__2].i - q__2.i; // , expr subst
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
}
kstep = 2;
}
if (kstep == 1)
{
/* Interchange rows and columns K and IPIV(K) in the trailing */
/* submatrix A(k-1:n,k-1:n) */
kp = ipiv[k];
if (kp != k)
{
if (kp < *n)
{
i__1 = *n - kp;
cswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + 1 + kp * a_dim1], &c__1);
}
i__1 = kp - k - 1;
cswap_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[kp + (k + 1) * a_dim1], lda);
i__1 = k + k * a_dim1;
temp.r = a[i__1].r;
temp.i = a[i__1].i; // , expr subst
i__1 = k + k * a_dim1;
i__2 = kp + kp * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = kp + kp * a_dim1;
a[i__1].r = temp.r;
a[i__1].i = temp.i; // , expr subst
}
}
else
{
/* Interchange rows and columns K and K-1 with -IPIV(K) and */
/* -IPIV(K-1) in the trailing submatrix A(k-1:n,k-1:n) */
kp = -ipiv[k];
if (kp != k)
{
if (kp < *n)
{
i__1 = *n - kp;
cswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + 1 + kp * a_dim1], &c__1);
}
i__1 = kp - k - 1;
cswap_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[kp + (k + 1) * a_dim1], lda);
i__1 = k + k * a_dim1;
temp.r = a[i__1].r;
temp.i = a[i__1].i; // , expr subst
i__1 = k + k * a_dim1;
i__2 = kp + kp * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = kp + kp * a_dim1;
a[i__1].r = temp.r;
a[i__1].i = temp.i; // , expr subst
i__1 = k + (k - 1) * a_dim1;
temp.r = a[i__1].r;
temp.i = a[i__1].i; // , expr subst
i__1 = k + (k - 1) * a_dim1;
i__2 = kp + (k - 1) * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = kp + (k - 1) * a_dim1;
a[i__1].r = temp.r;
a[i__1].i = temp.i; // , expr subst
}
--k;
kp = -ipiv[k];
if (kp != k)
{
if (kp < *n)
{
i__1 = *n - kp;
cswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + 1 + kp * a_dim1], &c__1);
}
i__1 = kp - k - 1;
cswap_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[kp + (k + 1) * a_dim1], lda);
i__1 = k + k * a_dim1;
temp.r = a[i__1].r;
temp.i = a[i__1].i; // , expr subst
i__1 = k + k * a_dim1;
i__2 = kp + kp * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = kp + kp * a_dim1;
a[i__1].r = temp.r;
a[i__1].i = temp.i; // , expr subst
}
}
--k;
goto L50;
L60:
;
}
return 0;
/* End of CSYTRI_ROOK */
}
/* Subroutine */ int cla_syrfsx_extended__(integer *prec_type__, char *uplo,
integer *n, integer *nrhs, complex *a, integer *lda, complex *af,
integer *ldaf, integer *ipiv, logical *colequ, real *c__, complex *b,
integer *ldb, complex *y, integer *ldy, real *berr_out__, integer *
n_norms__, real *err_bnds_norm__, real *err_bnds_comp__, complex *res,
real *ayb, complex *dy, complex *y_tail__, real *rcond, integer *
ithresh, real *rthresh, real *dz_ub__, logical *ignore_cwise__,
integer *info, ftnlen uplo_len)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, y_dim1,
y_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3, i__4;
real r__1, r__2;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
real dxratmax, dzratmax;
integer i__, j;
logical incr_prec__;
extern /* Subroutine */ int cla_syamv__(integer *, integer *, real *,
complex *, integer *, complex *, integer *, real *, real *,
integer *);
real prev_dz_z__, yk, final_dx_x__;
extern /* Subroutine */ int cla_wwaddw__(integer *, complex *, complex *,
complex *);
real final_dz_z__, prevnormdx;
integer cnt;
real dyk, eps, incr_thresh__, dx_x__, dz_z__;
extern /* Subroutine */ int cla_lin_berr__(integer *, integer *, integer *
, complex *, real *, real *);
real ymin;
integer y_prec_state__;
extern /* Subroutine */ int blas_csymv_x__(integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *, integer *);
integer uplo2;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int blas_csymv2_x__(integer *, integer *, complex
*, complex *, integer *, complex *, complex *, integer *, complex
*, complex *, integer *, integer *), ccopy_(integer *, complex *,
integer *, complex *, integer *);
real dxrat, dzrat;
extern /* Subroutine */ int caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *), csymv_(char *, integer *,
complex *, complex *, integer *, complex *, integer *, complex *,
complex *, integer *);
real normx, normy;
extern doublereal slamch_(char *);
real normdx;
extern /* Subroutine */ int csytrs_(char *, integer *, integer *, complex
*, integer *, integer *, complex *, integer *, integer *);
real hugeval;
extern integer ilauplo_(char *);
integer x_state__, z_state__;
/* -- 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 */
/* ======= */
/* CLA_SYRFSX_EXTENDED improves the computed solution to a system of */
/* linear equations by performing extra-precise iterative refinement */
/* and provides error bounds and backward error estimates for the solution. */
/* This subroutine is called by CSYRFSX to perform iterative refinement. */
/* 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. Note that this */
/* subroutine is only resonsible for setting the second fields of */
/* ERR_BNDS_NORM and ERR_BNDS_COMP. */
/* Arguments */
/* ========= */
/* PREC_TYPE (input) INTEGER */
/* Specifies the intermediate precision to be used in refinement. */
/* The value is defined by ILAPREC(P) where P is a CHARACTER and */
/* P = 'S': Single */
/* = 'D': Double */
/* = 'I': Indigenous */
/* = 'X', 'E': Extra */
/* 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. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input) COMPLEX array, dimension (LDAF,N) */
/* The block diagonal matrix D and the multipliers used to */
/* obtain the factor U or L as computed by CSYTRF. */
/* 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 CSYTRF. */
/* COLEQU (input) LOGICAL */
/* If .TRUE. then column equilibration was done to A before calling */
/* this routine. This is needed to compute the solution and error */
/* bounds correctly. */
/* C (input) REAL array, dimension (N) */
/* The column scale factors for A. If COLEQU = .FALSE., C */
/* is not accessed. If C is input, each element of C 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 array, dimension (LDB,NRHS) */
/* The right-hand-side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* Y (input/output) COMPLEX array, dimension */
/* (LDY,NRHS) */
/* On entry, the solution matrix X, as computed by CSYTRS. */
/* On exit, the improved solution matrix Y. */
/* LDY (input) INTEGER */
/* The leading dimension of the array Y. LDY >= max(1,N). */
/* BERR_OUT (output) REAL array, dimension (NRHS) */
/* On exit, BERR_OUT(j) contains the componentwise relative backward */
/* error for right-hand-side j from the formula */
/* max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. This is computed by CLA_LIN_BERR. */
/* N_NORMS (input) INTEGER */
/* Determines which error bounds to return (see ERR_BNDS_NORM */
/* and ERR_BNDS_COMP). */
/* If N_NORMS >= 1 return normwise error bounds. */
/* If N_NORMS >= 2 return componentwise error bounds. */
/* ERR_BNDS_NORM (input/output) REAL 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) * slamch('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) * slamch('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) * slamch('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. */
/* This subroutine is only responsible for setting the second field */
/* above. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* ERR_BNDS_COMP (input/output) REAL 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) * slamch('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) * slamch('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) * slamch('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. */
/* This subroutine is only responsible for setting the second field */
/* above. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* RES (input) COMPLEX array, dimension (N) */
/* Workspace to hold the intermediate residual. */
/* AYB (input) REAL array, dimension (N) */
/* Workspace. */
/* DY (input) COMPLEX array, dimension (N) */
/* Workspace to hold the intermediate solution. */
/* Y_TAIL (input) COMPLEX array, dimension (N) */
/* Workspace to hold the trailing bits of the intermediate solution. */
/* RCOND (input) REAL */
/* 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. */
/* ITHRESH (input) INTEGER */
/* The maximum number of residual computations allowed for */
/* refinement. The default is 10. For '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. */
/* RTHRESH (input) REAL */
/* Determines when to stop refinement if the error estimate stops */
/* decreasing. Refinement will stop when the next solution no longer */
/* satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */
/* the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */
/* default value is 0.5. For 'aggressive' set to 0.9 to permit */
/* convergence on extremely ill-conditioned matrices. See LAWN 165 */
/* for more details. */
/* DZ_UB (input) REAL */
/* Determines when to start considering componentwise convergence. */
/* Componentwise convergence is only considered after each component */
/* of the solution Y is stable, which we definte as the relative */
/* change in each component being less than DZ_UB. The default value */
/* is 0.25, requiring the first bit to be stable. See LAWN 165 for */
/* more details. */
/* IGNORE_CWISE (input) LOGICAL */
/* If .TRUE. then ignore componentwise convergence. Default value */
/* is .FALSE.. */
/* INFO (output) INTEGER */
/* = 0: Successful exit. */
/* < 0: if INFO = -i, the ith argument to CSYTRS had an illegal */
/* value */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Parameters .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1;
err_bnds_norm__ -= err_bnds_norm_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1;
y -= y_offset;
--berr_out__;
--res;
--ayb;
--dy;
--y_tail__;
/* Function Body */
if (*info != 0) {
return 0;
}
eps = slamch_("Epsilon");
hugeval = slamch_("Overflow");
/* Force HUGEVAL to Inf */
hugeval *= hugeval;
/* Using HUGEVAL may lead to spurious underflows. */
incr_thresh__ = (real) (*n) * eps;
if (lsame_(uplo, "L")) {
uplo2 = ilauplo_("L");
} else {
uplo2 = ilauplo_("U");
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
y_prec_state__ = 1;
if (y_prec_state__ == 2) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
y_tail__[i__3].r = 0.f, y_tail__[i__3].i = 0.f;
}
}
dxrat = 0.f;
dxratmax = 0.f;
dzrat = 0.f;
dzratmax = 0.f;
final_dx_x__ = hugeval;
final_dz_z__ = hugeval;
prevnormdx = hugeval;
prev_dz_z__ = hugeval;
dz_z__ = hugeval;
dx_x__ = hugeval;
x_state__ = 1;
z_state__ = 0;
incr_prec__ = FALSE_;
i__2 = *ithresh;
for (cnt = 1; cnt <= i__2; ++cnt) {
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
if (y_prec_state__ == 0) {
csymv_(uplo, n, &c_b11, &a[a_offset], lda, &y[j * y_dim1 + 1],
&c__1, &c_b12, &res[1], &c__1);
} else if (y_prec_state__ == 1) {
blas_csymv_x__(&uplo2, n, &c_b11, &a[a_offset], lda, &y[j *
y_dim1 + 1], &c__1, &c_b12, &res[1], &c__1,
prec_type__);
} else {
blas_csymv2_x__(&uplo2, n, &c_b11, &a[a_offset], lda, &y[j *
y_dim1 + 1], &y_tail__[1], &c__1, &c_b12, &res[1], &
c__1, prec_type__);
}
/* XXX: RES is no longer needed. */
ccopy_(n, &res[1], &c__1, &dy[1], &c__1);
csytrs_(uplo, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &dy[1], n,
info);
/* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */
normx = 0.f;
normy = 0.f;
normdx = 0.f;
dz_z__ = 0.f;
ymin = hugeval;
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * y_dim1;
yk = (r__1 = y[i__4].r, dabs(r__1)) + (r__2 = r_imag(&y[i__ +
j * y_dim1]), dabs(r__2));
i__4 = i__;
dyk = (r__1 = dy[i__4].r, dabs(r__1)) + (r__2 = r_imag(&dy[
i__]), dabs(r__2));
if (yk != 0.f) {
/* Computing MAX */
r__1 = dz_z__, r__2 = dyk / yk;
dz_z__ = dmax(r__1,r__2);
} else if (dyk != 0.f) {
dz_z__ = hugeval;
}
ymin = dmin(ymin,yk);
normy = dmax(normy,yk);
if (*colequ) {
/* Computing MAX */
r__1 = normx, r__2 = yk * c__[i__];
normx = dmax(r__1,r__2);
/* Computing MAX */
r__1 = normdx, r__2 = dyk * c__[i__];
normdx = dmax(r__1,r__2);
} else {
normx = normy;
normdx = dmax(normdx,dyk);
}
}
if (normx != 0.f) {
dx_x__ = normdx / normx;
} else if (normdx == 0.f) {
dx_x__ = 0.f;
} else {
dx_x__ = hugeval;
}
dxrat = normdx / prevnormdx;
dzrat = dz_z__ / prev_dz_z__;
/* Check termination criteria. */
if (ymin * *rcond < incr_thresh__ * normy && y_prec_state__ < 2) {
incr_prec__ = TRUE_;
}
if (x_state__ == 3 && dxrat <= *rthresh) {
x_state__ = 1;
}
if (x_state__ == 1) {
if (dx_x__ <= eps) {
x_state__ = 2;
} else if (dxrat > *rthresh) {
if (y_prec_state__ != 2) {
incr_prec__ = TRUE_;
} else {
x_state__ = 3;
}
} else {
if (dxrat > dxratmax) {
dxratmax = dxrat;
}
}
if (x_state__ > 1) {
final_dx_x__ = dx_x__;
}
}
if (z_state__ == 0 && dz_z__ <= *dz_ub__) {
z_state__ = 1;
}
if (z_state__ == 3 && dzrat <= *rthresh) {
z_state__ = 1;
}
if (z_state__ == 1) {
if (dz_z__ <= eps) {
z_state__ = 2;
} else if (dz_z__ > *dz_ub__) {
z_state__ = 0;
dzratmax = 0.f;
final_dz_z__ = hugeval;
} else if (dzrat > *rthresh) {
if (y_prec_state__ != 2) {
incr_prec__ = TRUE_;
} else {
z_state__ = 3;
}
} else {
if (dzrat > dzratmax) {
dzratmax = dzrat;
}
}
if (z_state__ > 1) {
final_dz_z__ = dz_z__;
}
}
if (x_state__ != 1 && (*ignore_cwise__ || z_state__ != 1)) {
goto L666;
}
if (incr_prec__) {
incr_prec__ = FALSE_;
++y_prec_state__;
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
y_tail__[i__4].r = 0.f, y_tail__[i__4].i = 0.f;
}
}
prevnormdx = normdx;
prev_dz_z__ = dz_z__;
/* Update soluton. */
if (y_prec_state__ < 2) {
caxpy_(n, &c_b12, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1);
} else {
cla_wwaddw__(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]);
}
}
/* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. */
L666:
/* Set final_* when cnt hits ithresh. */
if (x_state__ == 1) {
final_dx_x__ = dx_x__;
}
if (z_state__ == 1) {
final_dz_z__ = dz_z__;
}
/* Compute error bounds. */
if (*n_norms__ >= 1) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / (
1 - dxratmax);
}
if (*n_norms__ >= 2) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / (
1 - dzratmax);
}
/* Compute componentwise relative backward error from formula */
/* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. */
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
csymv_(uplo, n, &c_b11, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1,
&c_b12, &res[1], &c__1);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
ayb[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[i__
+ j * b_dim1]), dabs(r__2));
}
/* Compute abs(op(A_s))*abs(Y) + abs(B_s). */
cla_syamv__(&uplo2, n, &c_b33, &a[a_offset], lda, &y[j * y_dim1 + 1],
&c__1, &c_b33, &ayb[1], &c__1);
cla_lin_berr__(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]);
/* End of loop for each RHS. */
}
return 0;
} /* cla_syrfsx_extended__ */
