/* 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 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 csysvx_(char *fact, 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 *rcond,
real *ferr, real *berr, complex *work, integer *lwork, 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;
/* Local variables */
integer nb;
extern logical lsame_(char *, char *);
real anorm;
extern doublereal slamch_(char *);
logical nofact;
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), xerbla_(char *,
integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern doublereal clansy_(char *, char *, integer *, complex *, integer *,
real *);
extern /* Subroutine */ int csycon_(char *, integer *, complex *, integer
*, integer *, real *, real *, complex *, integer *),
csyrfs_(char *, integer *, integer *, complex *, integer *,
complex *, integer *, integer *, complex *, integer *, complex *,
integer *, real *, real *, complex *, real *, integer *),
csytrf_(char *, integer *, complex *, integer *, integer *,
complex *, integer *, integer *);
integer lwkopt;
logical lquery;
extern /* Subroutine */ int csytrs_(char *, integer *, integer *, complex
*, integer *, integer *, complex *, integer *, integer *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CSYSVX 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 symmetric 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**T, if UPLO = 'U', or */
/* A = L * D * L**T, if UPLO = 'L', */
/* where U (or L) is a product of permutation and unit upper (lower) */
/* triangular matrices, and D is symmetric and block diagonal with */
/* 1-by-1 and 2-by-2 diagonal blocks. */
/* 2. If some D(i,i)=0, so that D is exactly singular, then the routine */
/* returns with INFO = i. Otherwise, the factored form of A is used */
/* to estimate the condition number of the matrix A. If the */
/* reciprocal of the condition number is less than machine precision, */
/* INFO = N+1 is returned as a warning, but the routine still goes on */
/* to solve for X and compute error bounds as described below. */
/* 3. The system of equations is solved for X using the factored form */
/* of A. */
/* 4. Iterative refinement is applied to improve the computed solution */
/* matrix and calculate error bounds and backward error estimates */
/* for it. */
/* Arguments */
/* ========= */
/* FACT (input) CHARACTER*1 */
/* Specifies whether or not the factored form of A has been */
/* supplied on entry. */
/* = 'F': On entry, 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 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 or output) COMPLEX 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**T or A = L*D*L**T as computed by CSYTRF. */
/* 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**T or A = L*D*L**T. */
/* 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 CSYTRF. */
/* 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 CSYTRF. */
/* B (input) COMPLEX 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 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) REAL */
/* 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) 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/output) COMPLEX 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 CSYTRF. */
/* 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) REAL array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, and i is */
/* <= N: 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, "CSYTRF", 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 = (real) lwkopt, work[1].i = 0.f;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CSYSVX", &i__1);
return 0;
} else if (lquery) {
return 0;
}
if (nofact) {
/* Compute the factorization A = U*D*U' or A = L*D*L'. */
clacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
csytrf_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &work[1], lwork,
info);
/* Return if INFO is non-zero. */
if (*info > 0) {
*rcond = 0.f;
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = clansy_("I", uplo, n, &a[a_offset], lda, &rwork[1]);
/* Compute the reciprocal of the condition number of A. */
csycon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1],
info);
/* Compute the solution vectors X. */
clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
csytrs_(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. */
csyrfs_(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 < slamch_("Epsilon")) {
*info = *n + 1;
}
work[1].r = (real) lwkopt, work[1].i = 0.f;
return 0;
/* End of CSYSVX */
} /* csysvx_ */
/* Subroutine */
int csysv_(char *uplo, integer *n, integer *nrhs, complex *a, integer *lda, integer *ipiv, complex *b, integer *ldb, complex *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
extern /* Subroutine */
int xerbla_(char *, integer *), csytrf_( char *, integer *, complex *, integer *, integer *, complex *, integer *, integer *);
integer lwkopt;
logical lquery;
extern /* Subroutine */
int csytrs_(char *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *), csytrs2_(char *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, complex *, integer *);
/* -- LAPACK driver 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 .. */
/* .. */
/* ===================================================================== */
/* .. 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;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
if (! lsame_(uplo, "U") && ! 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 (*ldb < max(1,*n))
{
*info = -8;
}
else if (*lwork < 1 && ! lquery)
{
*info = -10;
}
if (*info == 0)
{
if (*n == 0)
{
lwkopt = 1;
}
else
{
csytrf_(uplo, n, &a[a_offset], lda, &ipiv[1], &work[1], &c_n1, info);
lwkopt = work[1].r;
}
work[1].r = (real) lwkopt;
work[1].i = 0.f; // , expr subst
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CSYSV ", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Compute the factorization A = U*D*U**T or A = L*D*L**T. */
csytrf_(uplo, n, &a[a_offset], lda, &ipiv[1], &work[1], lwork, info);
if (*info == 0)
{
/* Solve the system A*X = B, overwriting B with X. */
if (*lwork < *n)
{
/* Solve with TRS ( Use Level BLAS 2) */
csytrs_(uplo, n, nrhs, &a[a_offset], lda, &ipiv[1], &b[b_offset], ldb, info);
}
else
{
/* Solve with TRS2 ( Use Level BLAS 3) */
csytrs2_(uplo, n, nrhs, &a[a_offset], lda, &ipiv[1], &b[b_offset], ldb, &work[1], info);
}
}
work[1].r = (real) lwkopt;
work[1].i = 0.f; // , expr subst
return 0;
/* End of CSYSV */
}
/* ===================================================================== */
real cla_syrcond_c_(char *uplo, integer *n, complex *a, integer *lda, complex *af, integer *ldaf, integer *ipiv, real *c__, logical *capply, integer *info, complex *work, real *rwork)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, i__1, i__2, i__3, i__4;
real ret_val, r__1, r__2;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer i__, j;
logical up;
real tmp;
integer kase;
extern logical lsame_(char *, char *);
integer isave[3];
real anorm;
logical upper;
extern /* Subroutine */
int clacn2_(integer *, complex *, complex *, real *, integer *, integer *), xerbla_(char *, integer *);
real ainvnm;
extern /* Subroutine */
int csytrs_(char *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *);
/* -- 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 .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. Executable Statements .. */
/* 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;
--c__;
--work;
--rwork;
/* Function Body */
ret_val = 0.f;
*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;
}
else if (*ldaf < max(1,*n))
{
*info = -6;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CLA_SYRCOND_C", &i__1);
return ret_val;
}
up = FALSE_;
if (lsame_(uplo, "U"))
{
up = TRUE_;
}
/* Compute norm of op(A)*op2(C). */
anorm = 0.f;
if (up)
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
tmp = 0.f;
if (*capply)
{
i__2 = i__;
for (j = 1;
j <= i__2;
++j)
{
i__3 = j + i__ * a_dim1;
tmp += ((r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[ j + i__ * a_dim1]), abs(r__2))) / c__[j];
}
i__2 = *n;
for (j = i__ + 1;
j <= i__2;
++j)
{
i__3 = i__ + j * a_dim1;
tmp += ((r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[ i__ + j * a_dim1]), abs(r__2))) / c__[j];
}
}
else
{
i__2 = i__;
for (j = 1;
j <= i__2;
++j)
{
i__3 = j + i__ * a_dim1;
tmp += (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[ j + i__ * a_dim1]), abs(r__2));
}
i__2 = *n;
for (j = i__ + 1;
j <= i__2;
++j)
{
i__3 = i__ + j * a_dim1;
tmp += (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[ i__ + j * a_dim1]), abs(r__2));
}
}
rwork[i__] = tmp;
anorm = max(anorm,tmp);
}
}
else
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
tmp = 0.f;
if (*capply)
{
i__2 = i__;
for (j = 1;
j <= i__2;
++j)
{
i__3 = i__ + j * a_dim1;
tmp += ((r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[ i__ + j * a_dim1]), abs(r__2))) / c__[j];
}
i__2 = *n;
for (j = i__ + 1;
j <= i__2;
++j)
{
i__3 = j + i__ * a_dim1;
tmp += ((r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[ j + i__ * a_dim1]), abs(r__2))) / c__[j];
}
}
else
{
i__2 = i__;
for (j = 1;
j <= i__2;
++j)
{
i__3 = i__ + j * a_dim1;
tmp += (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[ i__ + j * a_dim1]), abs(r__2));
}
i__2 = *n;
for (j = i__ + 1;
j <= i__2;
++j)
{
i__3 = j + i__ * a_dim1;
tmp += (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag(&a[ j + i__ * a_dim1]), abs(r__2));
}
}
rwork[i__] = tmp;
anorm = max(anorm,tmp);
}
}
/* Quick return if possible. */
if (*n == 0)
{
ret_val = 1.f;
return ret_val;
}
else if (anorm == 0.f)
{
return ret_val;
}
/* Estimate the norm of inv(op(A)). */
ainvnm = 0.f;
kase = 0;
L10:
clacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
if (kase != 0)
{
if (kase == 2)
{
/* Multiply by R. */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
i__2 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = rwork[i__4] * work[i__3].r;
q__1.i = rwork[i__4] * work[i__3].i; // , expr subst
work[i__2].r = q__1.r;
work[i__2].i = q__1.i; // , expr subst
}
if (up)
{
csytrs_("U", n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[ 1], n, info);
}
else
{
csytrs_("L", n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[ 1], n, info);
}
/* Multiply by inv(C). */
if (*capply)
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
i__2 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = c__[i__4] * work[i__3].r;
q__1.i = c__[i__4] * work[i__3].i; // , expr subst
work[i__2].r = q__1.r;
work[i__2].i = q__1.i; // , expr subst
}
}
}
else
{
/* Multiply by inv(C**T). */
if (*capply)
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
i__2 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = c__[i__4] * work[i__3].r;
q__1.i = c__[i__4] * work[i__3].i; // , expr subst
work[i__2].r = q__1.r;
work[i__2].i = q__1.i; // , expr subst
}
}
if (up)
{
csytrs_("U", n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[ 1], n, info);
}
else
{
csytrs_("L", n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[ 1], n, info);
}
/* Multiply by R. */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
i__2 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = rwork[i__4] * work[i__3].r;
q__1.i = rwork[i__4] * work[i__3].i; // , expr subst
work[i__2].r = q__1.r;
work[i__2].i = q__1.i; // , expr subst
}
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.f)
{
ret_val = 1.f / ainvnm;
}
return ret_val;
}
/* Subroutine */
int csysvx_(char *fact, 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 *rcond, real *ferr, real *berr, complex *work, integer *lwork, 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;
/* Local variables */
integer nb;
extern logical lsame_(char *, char *);
real anorm;
extern real slamch_(char *);
logical nofact;
extern /* Subroutine */
int clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
extern real clansy_(char *, char *, integer *, complex *, integer *, real *);
extern /* Subroutine */
int csycon_(char *, integer *, complex *, integer *, integer *, real *, real *, complex *, integer *), csyrfs_(char *, integer *, integer *, complex *, integer *, complex *, integer *, integer *, complex *, integer *, complex *, integer *, real *, real *, complex *, real *, integer *), csytrf_(char *, integer *, complex *, integer *, integer *, complex *, integer *, integer *);
integer lwkopt;
logical lquery;
extern /* Subroutine */
int csytrs_(char *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *);
/* -- LAPACK driver routine (version 3.4.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* April 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* 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; // , expr subst
if (*lwork < max(i__1,i__2) && ! lquery)
{
*info = -18;
}
}
if (*info == 0)
{
/* Computing MAX */
i__1 = 1;
i__2 = *n << 1; // , expr subst
lwkopt = max(i__1,i__2);
if (nofact)
{
nb = ilaenv_(&c__1, "CSYTRF", uplo, n, &c_n1, &c_n1, &c_n1);
/* Computing MAX */
i__1 = lwkopt;
i__2 = *n * nb; // , expr subst
lwkopt = max(i__1,i__2);
}
work[1].r = (real) lwkopt;
work[1].i = 0.f; // , expr subst
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CSYSVX", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
if (nofact)
{
/* Compute the factorization A = U*D*U**T or A = L*D*L**T. */
clacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
csytrf_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &work[1], lwork, info);
/* Return if INFO is non-zero. */
if (*info > 0)
{
*rcond = 0.f;
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = clansy_("I", uplo, n, &a[a_offset], lda, &rwork[1]);
/* Compute the reciprocal of the condition number of A. */
csycon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1], info);
/* Compute the solution vectors X. */
clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
csytrs_(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. */
csyrfs_(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 < slamch_("Epsilon"))
{
*info = *n + 1;
}
work[1].r = (real) lwkopt;
work[1].i = 0.f; // , expr subst
return 0;
/* End of CSYSVX */
}
int csycon_(char *uplo, int *n, complex *a, int *lda,
int *ipiv, float *anorm, float *rcond, complex *work, int *
info)
{
/* System generated locals */
int a_dim1, a_offset, i__1, i__2;
/* Local variables */
int i__, kase;
extern int lsame_(char *, char *);
int isave[3];
int upper;
extern int clacn2_(int *, complex *, complex *, float
*, int *, int *), xerbla_(char *, int *);
float ainvnm;
extern int csytrs_(char *, int *, int *, complex
*, int *, int *, complex *, int *, int *);
/* -- 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 */
/* ======= */
/* CSYCON estimates the reciprocal of the condition number (in the */
/* 1-norm) of a complex symmetric matrix A using the factorization */
/* A = U*D*U**T or A = L*D*L**T computed by CSYTRF. */
/* An estimate is obtained for norm(inv(A)), and the reciprocal of the */
/* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the details of the factorization are stored */
/* as an upper or lower triangular matrix. */
/* = 'U': Upper triangular, form is A = U*D*U**T; */
/* = 'L': Lower triangular, form is A = L*D*L**T. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* The block diagonal matrix D and the multipliers used to */
/* obtain the factor U or L as computed by CSYTRF. */
/* 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. */
/* ANORM (input) REAL */
/* The 1-norm of the original matrix A. */
/* RCOND (output) REAL */
/* The reciprocal of the condition number of the matrix A, */
/* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an */
/* estimate of the 1-norm of inv(A) computed in this routine. */
/* WORK (workspace) 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 .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. 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;
} else if (*anorm < 0.f) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CSYCON", &i__1);
return 0;
}
/* Quick return if possible */
*rcond = 0.f;
if (*n == 0) {
*rcond = 1.f;
return 0;
} else if (*anorm <= 0.f) {
return 0;
}
/* Check that the diagonal matrix D is nonsingular. */
if (upper) {
/* Upper triangular storage: examine D from bottom to top */
for (i__ = *n; i__ >= 1; --i__) {
i__1 = i__ + i__ * a_dim1;
if (ipiv[i__] > 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 (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * a_dim1;
if (ipiv[i__] > 0 && (a[i__2].r == 0.f && a[i__2].i == 0.f)) {
return 0;
}
/* L20: */
}
}
/* Estimate the 1-norm of the inverse. */
kase = 0;
L30:
clacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
if (kase != 0) {
/* Multiply by inv(L*D*L') or inv(U*D*U'). */
csytrs_(uplo, n, &c__1, &a[a_offset], lda, &ipiv[1], &work[1], n,
info);
goto L30;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.f) {
*rcond = 1.f / ainvnm / *anorm;
}
return 0;
/* End of CSYCON */
} /* csycon_ */
/* Subroutine */ int csycon_(char *uplo, integer *n, complex *a, integer *lda,
integer *ipiv, real *anorm, real *rcond, 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
March 31, 1993
Purpose
=======
CSYCON estimates the reciprocal of the condition number (in the
1-norm) of a complex symmetric matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by CSYTRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
Arguments
=========
UPLO (input) CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= 'U': Upper triangular, form is A = U*D*U**T;
= 'L': Lower triangular, form is A = L*D*L**T.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input) COMPLEX array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by CSYTRF.
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.
ANORM (input) REAL
The 1-norm of the original matrix A.
RCOND (output) REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.
WORK (workspace) 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 parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer kase, i__;
extern logical lsame_(char *, char *);
static logical upper;
extern /* Subroutine */ int clacon_(integer *, complex *, complex *, real
*, integer *), xerbla_(char *, integer *);
static real ainvnm;
extern /* Subroutine */ int csytrs_(char *, integer *, integer *, complex
*, integer *, integer *, complex *, integer *, integer *);
#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;
} else if (*anorm < 0.f) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CSYCON", &i__1);
return 0;
}
/* Quick return if possible */
*rcond = 0.f;
if (*n == 0) {
*rcond = 1.f;
return 0;
} else if (*anorm <= 0.f) {
return 0;
}
/* Check that the diagonal matrix D is nonsingular. */
if (upper) {
/* Upper triangular storage: examine D from bottom to top */
for (i__ = *n; i__ >= 1; --i__) {
i__1 = a_subscr(i__, i__);
if (ipiv[i__] > 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 (i__ = 1; i__ <= i__1; ++i__) {
i__2 = a_subscr(i__, i__);
if (ipiv[i__] > 0 && (a[i__2].r == 0.f && a[i__2].i == 0.f)) {
return 0;
}
/* L20: */
}
}
/* Estimate the 1-norm of the inverse. */
kase = 0;
L30:
clacon_(n, &work[*n + 1], &work[1], &ainvnm, &kase);
if (kase != 0) {
/* Multiply by inv(L*D*L') or inv(U*D*U'). */
csytrs_(uplo, n, &c__1, &a[a_offset], lda, &ipiv[1], &work[1], n,
info);
goto L30;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.f) {
*rcond = 1.f / ainvnm / *anorm;
}
return 0;
/* End of CSYCON */
} /* csycon_ */
/* 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__ */
/* Subroutine */ int cchksy_(logical *dotype, integer *nn, integer *nval,
integer *nnb, integer *nbval, integer *nns, integer *nsval, real *
thresh, logical *tsterr, integer *nmax, complex *a, complex *afac,
complex *ainv, complex *b, complex *x, complex *xact, complex *work,
real *rwork, integer *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 *), cget04_(
integer *, integer *, complex *, integer *, complex *, integer *,
real *, real *);
integer nfail, iseed[4];
real rcond;
integer nimat;
extern doublereal sget06_(real *, real *);
extern /* Subroutine */ int cpot05_(char *, integer *, integer *, complex
*, integer *, complex *, integer *, complex *, integer *, complex
*, integer *, real *, real *, real *);
real anorm;
extern /* Subroutine */ int csyt01_(char *, integer *, complex *, integer
*, complex *, integer *, integer *, complex *, integer *, real *,
real *), csyt02_(char *, integer *, integer *, complex *,
integer *, complex *, integer *, complex *, integer *, real *,
real *), csyt03_(char *, integer *, complex *, integer *,
complex *, integer *, complex *, integer *, real *, real *, real *
);
integer iuplo, izero, nerrs, lwork;
logical zerot;
char xtype[1];
extern /* Subroutine */ int clatb4_(char *, integer *, integer *, integer
*, char *, integer *, integer *, real *, integer *, real *, char *
), alaerh_(char *, char *, integer *,
integer *, char *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *, integer *, integer *);
real rcondc;
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), clarhs_(char *, char
*, char *, char *, integer *, integer *, integer *, integer *,
integer *, complex *, integer *, complex *, integer *, complex *,
integer *, integer *, integer *),
alasum_(char *, integer *, integer *, integer *, integer *);
real cndnum;
extern /* Subroutine */ int clatms_(integer *, integer *, char *, integer
*, char *, real *, integer *, real *, real *, integer *, integer *
, char *, complex *, integer *, complex *, integer *);
extern doublereal clansy_(char *, char *, integer *, complex *, integer *,
real *);
logical trfcon;
extern /* Subroutine */ int csycon_(char *, integer *, complex *, integer
*, integer *, real *, real *, complex *, integer *),
clatsy_(char *, integer *, complex *, integer *, integer *), xlaenv_(integer *, integer *), cerrsy_(char *, integer *), csyrfs_(char *, integer *, integer *, complex *,
integer *, complex *, integer *, integer *, complex *, integer *,
complex *, integer *, real *, real *, complex *, real *, integer *
), csytrf_(char *, integer *, complex *, integer *,
integer *, complex *, integer *, integer *), csytri_(char
*, integer *, complex *, integer *, integer *, complex *, integer
*);
real result[8];
extern /* Subroutine */ int csytrs_(char *, integer *, integer *, complex
*, integer *, integer *, complex *, 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 */
/* ======= */
/* CCHKSY tests CSYTRF, -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) REAL */
/* The threshold value for the test ratios. A result is */
/* included in the output file if RESULT >= THRESH. To have */
/* every test ratio printed, use THRESH = 0. */
/* TSTERR (input) LOGICAL */
/* Flag that indicates whether error exits are to be tested. */
/* NMAX (input) INTEGER */
/* The maximum value permitted for N, used in dimensioning the */
/* work arrays. */
/* A (workspace) COMPLEX array, dimension (NMAX*NMAX) */
/* AFAC (workspace) COMPLEX array, dimension (NMAX*NMAX) */
/* AINV (workspace) COMPLEX array, dimension (NMAX*NMAX) */
/* B (workspace) COMPLEX array, dimension (NMAX*NSMAX) */
/* where NSMAX is the largest entry in NSVAL. */
/* X (workspace) COMPLEX array, dimension (NMAX*NSMAX) */
/* XACT (workspace) COMPLEX array, dimension (NMAX*NSMAX) */
/* WORK (workspace) COMPLEX array, dimension */
/* (NMAX*max(2,NSMAX)) */
/* RWORK (workspace) REAL array, */
/* dimension (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, "Complex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "SY", (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) {
cerrsy_(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 = 11;
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];
if (imat != 11) {
/* Set up parameters with CLATB4 and generate a test */
/* matrix with CLATMS. */
clatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &
mode, &cndnum, dist);
s_copy(srnamc_1.srnamt, "CLATMS", (ftnlen)6, (ftnlen)6);
clatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &
cndnum, &anorm, &kl, &ku, "N", &a[1], &lda, &work[
1], &info);
/* Check error code from CLATMS. */
if (info != 0) {
alaerh_(path, "CLATMS", &info, &c__0, uplo, &n, &n, &
c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs,
nout);
goto 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.f, a[i__4].i = 0.f;
/* L20: */
}
ioff += izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
i__4 = ioff;
a[i__4].r = 0.f, a[i__4].i = 0.f;
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.f, a[i__4].i = 0.f;
ioff += lda;
/* L40: */
}
ioff -= izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
i__4 = ioff + i__;
a[i__4].r = 0.f, a[i__4].i = 0.f;
/* L50: */
}
}
} else {
if (iuplo == 1) {
/* Set the first IZERO rows to zero. */
ioff = 0;
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.f, a[i__5].i = 0.f;
/* L60: */
}
ioff += lda;
/* L70: */
}
} else {
/* Set the last IZERO rows to zero. */
ioff = 0;
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.f, a[i__5].i = 0.f;
/* L80: */
}
ioff += lda;
/* L90: */
}
}
}
} else {
izero = 0;
}
} else {
/* Use a special block diagonal matrix to test alternate */
/* code for the 2 x 2 blocks. */
clatsy_(uplo, &n, &a[1], &lda, iseed);
}
/* 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. */
clacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda);
lwork = max(2,nb) * lda;
s_copy(srnamc_1.srnamt, "CSYTRF", (ftnlen)6, (ftnlen)6);
csytrf_(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 CSYTRF. */
if (info != k) {
alaerh_(path, "CSYTRF", &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. */
csyt01_(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) {
clacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda);
s_copy(srnamc_1.srnamt, "CSYTRI", (ftnlen)6, (ftnlen)
6);
csytri_(uplo, &n, &ainv[1], &lda, &iwork[1], &work[1],
&info);
/* Check error code from CSYTRI. */
if (info != 0) {
alaerh_(path, "CSYTRI", &info, &c__0, uplo, &n, &
n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &
nerrs, nout);
}
csyt03_(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(real));
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.f;
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, "CLARHS", (ftnlen)6, (ftnlen)
6);
clarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, &
nrhs, &a[1], &lda, &xact[1], &lda, &b[1], &
lda, iseed, &info);
clacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda);
s_copy(srnamc_1.srnamt, "CSYTRS", (ftnlen)6, (ftnlen)
6);
csytrs_(uplo, &n, &nrhs, &afac[1], &lda, &iwork[1], &
x[1], &lda, &info);
/* Check error code from CSYTRS. */
if (info != 0) {
alaerh_(path, "CSYTRS", &info, &c__0, uplo, &n, &
n, &c_n1, &c_n1, &nrhs, &imat, &nfail, &
nerrs, nout);
}
clacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &
lda);
csyt02_(uplo, &n, &nrhs, &a[1], &lda, &x[1], &lda, &
work[1], &lda, &rwork[1], &result[2]);
/* + TEST 4 */
/* Check solution from generated exact solution. */
cget04_(&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, "CSYRFS", (ftnlen)6, (ftnlen)
6);
csyrfs_(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 CSYRFS. */
if (info != 0) {
alaerh_(path, "CSYRFS", &info, &c__0, uplo, &n, &
n, &c_n1, &c_n1, &nrhs, &imat, &nfail, &
nerrs, nout);
}
cget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[4]);
cpot05_(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(real));
e_wsfe();
++nfail;
}
/* L120: */
}
nrun += 5;
/* L130: */
}
/* + TEST 8 */
/* Get an estimate of RCOND = 1/CNDNUM. */
L140:
anorm = clansy_("1", uplo, &n, &a[1], &lda, &rwork[1]);
s_copy(srnamc_1.srnamt, "CSYCON", (ftnlen)6, (ftnlen)6);
csycon_(uplo, &n, &afac[1], &lda, &iwork[1], &anorm, &
rcond, &work[1], &info);
/* Check error code from CSYCON. */
if (info != 0) {
alaerh_(path, "CSYCON", &info, &c__0, uplo, &n, &n, &
c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs,
nout);
}
result[7] = sget06_(&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(real)
);
e_wsfe();
++nfail;
}
++nrun;
L150:
;
}
L160:
;
}
L170:
;
}
/* L180: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of CCHKSY */
} /* cchksy_ */
