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OpenBLAS/lapack-netlib/SRC/ssyrfsx.c

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/* f2c.h -- Standard Fortran to C header file */
/** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed."
- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
#ifndef F2C_INCLUDE
#define F2C_INCLUDE
#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif
#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif
#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif
typedef blasint integer;
typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef blasint logical;
typedef char logical1;
typedef char integer1;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
typedef int flag;
typedef int ftnlen;
typedef int ftnint;
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
integer1 g;
shortint h;
integer i;
/* longint j; */
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
ftnlen *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b) ((a) >> (b) & 1)
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimag(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
/* procedure parameter types for -A and -C++ */
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif
static float spow_ui(float x, integer n) {
float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static double dpow_ui(double x, integer n) {
double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static _Complex float cpow_ui(_Complex float x, integer n) {
_Complex float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static _Complex double zpow_ui(_Complex double x, integer n) {
_Complex double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static integer pow_ii(integer x, integer n) {
integer pow; unsigned long int u;
if (n <= 0) {
if (n == 0 || x == 1) pow = 1;
else if (x != -1) pow = x == 0 ? 1/x : 0;
else n = -n;
}
if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
u = n;
for(pow = 1; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
double m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
float m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i]) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i]) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* Table of constant values */
static integer c_n1 = -1;
static integer c__0 = 0;
static integer c__1 = 1;
/* > \brief \b SSYRFSX */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SSYRFSX + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssyrfsx
.f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssyrfsx
.f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssyrfsx
.f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SSYRFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV, */
/* S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS, */
/* ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, */
/* WORK, IWORK, INFO ) */
/* CHARACTER UPLO, EQUED */
/* INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS, */
/* $ N_ERR_BNDS */
/* REAL RCOND */
/* INTEGER IPIV( * ), IWORK( * ) */
/* REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ), */
/* $ X( LDX, * ), WORK( * ) */
/* REAL S( * ), PARAMS( * ), BERR( * ), */
/* $ ERR_BNDS_NORM( NRHS, * ), */
/* $ ERR_BNDS_COMP( NRHS, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SSYRFSX 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. In addition to normwise error bound, the code provides */
/* > maximum componentwise error bound if possible. See comments for */
/* > ERR_BNDS_NORM and ERR_BNDS_COMP for details of the error bounds. */
/* > */
/* > The original system of linear equations may have been equilibrated */
/* > before calling this routine, as described by arguments EQUED and S */
/* > below. In this case, the solution and error bounds returned are */
/* > for the original unequilibrated system. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \verbatim */
/* > Some optional parameters are bundled in the PARAMS array. These */
/* > settings determine how refinement is performed, but often the */
/* > defaults are acceptable. If the defaults are acceptable, users */
/* > can pass NPARAMS = 0 which prevents the source code from accessing */
/* > the PARAMS argument. */
/* > \endverbatim */
/* > */
/* > \param[in] UPLO */
/* > \verbatim */
/* > UPLO is CHARACTER*1 */
/* > = 'U': Upper triangle of A is stored; */
/* > = 'L': Lower triangle of A is stored. */
/* > \endverbatim */
/* > */
/* > \param[in] EQUED */
/* > \verbatim */
/* > EQUED is CHARACTER*1 */
/* > Specifies the form of equilibration that was done to A */
/* > before calling this routine. This is needed to compute */
/* > the solution and error bounds correctly. */
/* > = 'N': No equilibration */
/* > = 'Y': Both row and column equilibration, i.e., A has been */
/* > replaced by diag(S) * A * diag(S). */
/* > The right hand side B has been changed accordingly. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NRHS */
/* > \verbatim */
/* > NRHS is INTEGER */
/* > The number of right hand sides, i.e., the number of columns */
/* > of the matrices B and X. NRHS >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] A */
/* > \verbatim */
/* > A is REAL 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. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] AF */
/* > \verbatim */
/* > AF is REAL 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 SSYTRF. */
/* > \endverbatim */
/* > */
/* > \param[in] LDAF */
/* > \verbatim */
/* > LDAF is INTEGER */
/* > The leading dimension of the array AF. LDAF >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] IPIV */
/* > \verbatim */
/* > IPIV is INTEGER array, dimension (N) */
/* > Details of the interchanges and the block structure of D */
/* > as determined by SSYTRF. */
/* > \endverbatim */
/* > */
/* > \param[in,out] S */
/* > \verbatim */
/* > S is REAL array, dimension (N) */
/* > The scale factors for A. If EQUED = 'Y', A is multiplied on */
/* > the left and right by diag(S). S is an input argument if FACT = */
/* > 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED */
/* > = 'Y', each element of S must be positive. If S is output, each */
/* > element of S is a power of the radix. If S is input, each element */
/* > of S should be a power of the radix to ensure a reliable solution */
/* > and error estimates. Scaling by powers of the radix does not cause */
/* > rounding errors unless the result underflows or overflows. */
/* > Rounding errors during scaling lead to refining with a matrix that */
/* > is not equivalent to the input matrix, producing error estimates */
/* > that may not be reliable. */
/* > \endverbatim */
/* > */
/* > \param[in] B */
/* > \verbatim */
/* > B is REAL array, dimension (LDB,NRHS) */
/* > The right hand side matrix B. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] X */
/* > \verbatim */
/* > X is REAL array, dimension (LDX,NRHS) */
/* > On entry, the solution matrix X, as computed by SGETRS. */
/* > On exit, the improved solution matrix X. */
/* > \endverbatim */
/* > */
/* > \param[in] LDX */
/* > \verbatim */
/* > LDX is INTEGER */
/* > The leading dimension of the array X. LDX >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] RCOND */
/* > \verbatim */
/* > RCOND is 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. */
/* > \endverbatim */
/* > */
/* > \param[out] BERR */
/* > \verbatim */
/* > BERR is REAL array, dimension (NRHS) */
/* > Componentwise relative backward error. This is the */
/* > componentwise relative backward error of each solution vector X(j) */
/* > (i.e., the smallest relative change in any element of A or B that */
/* > makes X(j) an exact solution). */
/* > \endverbatim */
/* > */
/* > \param[in] N_ERR_BNDS */
/* > \verbatim */
/* > N_ERR_BNDS is INTEGER */
/* > Number of error bounds to return for each right hand side */
/* > and each type (normwise or componentwise). See ERR_BNDS_NORM and */
/* > ERR_BNDS_COMP below. */
/* > \endverbatim */
/* > */
/* > \param[out] ERR_BNDS_NORM */
/* > \verbatim */
/* > ERR_BNDS_NORM is 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. */
/* > */
/* > See Lapack Working Note 165 for further details and extra */
/* > cautions. */
/* > \endverbatim */
/* > */
/* > \param[out] ERR_BNDS_COMP */
/* > \verbatim */
/* > ERR_BNDS_COMP is 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 < 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. */
/* > */
/* > See Lapack Working Note 165 for further details and extra */
/* > cautions. */
/* > \endverbatim */
/* > */
/* > \param[in] NPARAMS */
/* > \verbatim */
/* > NPARAMS is INTEGER */
/* > Specifies the number of parameters set in PARAMS. If <= 0, the */
/* > PARAMS array is never referenced and default values are used. */
/* > \endverbatim */
/* > */
/* > \param[in,out] PARAMS */
/* > \verbatim */
/* > PARAMS is REAL array, dimension NPARAMS */
/* > Specifies algorithm parameters. If an entry is < 0.0, then */
/* > that entry will be filled with default value used for that */
/* > parameter. Only positions up to NPARAMS are accessed; defaults */
/* > are used for higher-numbered parameters. */
/* > */
/* > PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */
/* > refinement or not. */
/* > Default: 1.0 */
/* > = 0.0: No refinement is performed, and no error bounds are */
/* > computed. */
/* > = 1.0: Use the double-precision refinement algorithm, */
/* > possibly with doubled-single computations if the */
/* > compilation environment does not support DOUBLE */
/* > PRECISION. */
/* > (other values are reserved for future use) */
/* > */
/* > PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */
/* > computations allowed for refinement. */
/* > Default: 10 */
/* > Aggressive: Set to 100 to permit convergence using approximate */
/* > factorizations or factorizations other than LU. If */
/* > the factorization uses a technique other than */
/* > Gaussian elimination, the guarantees in */
/* > err_bnds_norm and err_bnds_comp may no longer be */
/* > trustworthy. */
/* > */
/* > PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */
/* > will attempt to find a solution with small componentwise */
/* > relative error in the double-precision algorithm. Positive */
/* > is true, 0.0 is false. */
/* > Default: 1.0 (attempt componentwise convergence) */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (4*N) */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: Successful exit. The solution to every right-hand side is */
/* > guaranteed. */
/* > < 0: If INFO = -i, the i-th argument had an illegal value */
/* > > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */
/* > has been completed, but the factor U is exactly singular, so */
/* > the solution and error bounds could not be computed. RCOND = 0 */
/* > is returned. */
/* > = N+J: The solution corresponding to the Jth right-hand side is */
/* > not guaranteed. The solutions corresponding to other right- */
/* > hand sides K with K > J may not be guaranteed as well, but */
/* > only the first such right-hand side is reported. If a small */
/* > componentwise error is not requested (PARAMS(3) = 0.0) then */
/* > the Jth right-hand side is the first with a normwise error */
/* > bound that is not guaranteed (the smallest J such */
/* > that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */
/* > the Jth right-hand side is the first with either a normwise or */
/* > componentwise error bound that is not guaranteed (the smallest */
/* > J such that either ERR_BNDS_NORM(J,1) = 0.0 or */
/* > ERR_BNDS_COMP(J,1) = 0.0). See the definition of */
/* > ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */
/* > about all of the right-hand sides check ERR_BNDS_NORM or */
/* > ERR_BNDS_COMP. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date April 2012 */
/* > \ingroup realSYcomputational */
/* ===================================================================== */
/* Subroutine */ void ssyrfsx_(char *uplo, char *equed, integer *n, integer *
nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv,
real *s, real *b, integer *ldb, real *x, integer *ldx, real *rcond,
real *berr, integer *n_err_bnds__, real *err_bnds_norm__, real *
err_bnds_comp__, integer *nparams, real *params, real *work, integer *
iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
err_bnds_comp_dim1, err_bnds_comp_offset, i__1;
real r__1, r__2;
/* Local variables */
real illrcond_thresh__, unstable_thresh__, err_lbnd__;
extern /* Subroutine */ void sla_syrfsx_extended_(integer *, char *,
integer *, integer *, real *, integer *, real *, integer *,
integer *, logical *, real *, real *, integer *, real *, integer *
, real *, integer *, real *, real *, real *, real *, real *, real
*, real *, integer *, real *, real *, logical *, integer *);
char norm[1];
integer ref_type__;
logical ignore_cwise__;
integer j;
extern logical lsame_(char *, char *);
real anorm;
logical rcequ;
real rcond_tmp__;
integer prec_type__;
extern real slamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern real slansy_(char *, char *, integer *, real *, integer *, real *);
extern /* Subroutine */ void ssycon_(char *, integer *, real *, integer *,
integer *, real *, real *, real *, integer *, integer *);
extern integer ilaprec_(char *);
integer ithresh, n_norms__;
real rthresh;
extern real sla_syrcond_(char *, integer *, real *, integer *, real *,
integer *, integer *, integer *, real *, integer *, real *,
integer *);
real cwise_wrong__;
/* -- LAPACK computational routine (version 3.7.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* April 2012 */
/* ================================================================== */
/* Check the input parameters. */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1 * 1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1 * 1;
err_bnds_norm__ -= err_bnds_norm_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1 * 1;
af -= af_offset;
--ipiv;
--s;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
--berr;
--params;
--work;
--iwork;
/* Function Body */
*info = 0;
ref_type__ = 1;
if (*nparams >= 1) {
if (params[1] < 0.f) {
params[1] = 1.f;
} else {
ref_type__ = params[1];
}
}
/* Set default parameters. */
illrcond_thresh__ = (real) (*n) * slamch_("Epsilon");
ithresh = 10;
rthresh = .5f;
unstable_thresh__ = .25f;
ignore_cwise__ = FALSE_;
if (*nparams >= 2) {
if (params[2] < 0.f) {
params[2] = (real) ithresh;
} else {
ithresh = (integer) params[2];
}
}
if (*nparams >= 3) {
if (params[3] < 0.f) {
if (ignore_cwise__) {
params[3] = 0.f;
} else {
params[3] = 1.f;
}
} else {
ignore_cwise__ = params[3] == 0.f;
}
}
if (ref_type__ == 0 || *n_err_bnds__ == 0) {
n_norms__ = 0;
} else if (ignore_cwise__) {
n_norms__ = 1;
} else {
n_norms__ = 2;
}
rcequ = lsame_(equed, "Y");
/* Test input parameters. */
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! rcequ && ! lsame_(equed, "N")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*lda < f2cmax(1,*n)) {
*info = -6;
} else if (*ldaf < f2cmax(1,*n)) {
*info = -8;
} else if (*ldb < f2cmax(1,*n)) {
*info = -12;
} else if (*ldx < f2cmax(1,*n)) {
*info = -14;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSYRFSX", &i__1, (ftnlen)7);
return;
}
/* Quick return if possible. */
if (*n == 0 || *nrhs == 0) {
*rcond = 1.f;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
berr[j] = 0.f;
if (*n_err_bnds__ >= 1) {
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f;
}
if (*n_err_bnds__ >= 2) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.f;
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.f;
}
if (*n_err_bnds__ >= 3) {
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.f;
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.f;
}
}
return;
}
/* Default to failure. */
*rcond = 0.f;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
berr[j] = 1.f;
if (*n_err_bnds__ >= 1) {
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f;
}
if (*n_err_bnds__ >= 2) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f;
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f;
}
if (*n_err_bnds__ >= 3) {
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.f;
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.f;
}
}
/* Compute the norm of A and the reciprocal of the condition */
/* number of A. */
*(unsigned char *)norm = 'I';
anorm = slansy_(norm, uplo, n, &a[a_offset], lda, &work[1]);
ssycon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1],
&iwork[1], info);
/* Perform refinement on each right-hand side */
if (ref_type__ != 0) {
prec_type__ = ilaprec_("D");
sla_syrfsx_extended_(&prec_type__, uplo, n, nrhs, &a[a_offset], lda,
&af[af_offset], ldaf, &ipiv[1], &rcequ, &s[1], &b[b_offset],
ldb, &x[x_offset], ldx, &berr[1], &n_norms__, &
err_bnds_norm__[err_bnds_norm_offset], &err_bnds_comp__[
err_bnds_comp_offset], &work[*n + 1], &work[1], &work[(*n <<
1) + 1], &work[1], rcond, &ithresh, &rthresh, &
unstable_thresh__, &ignore_cwise__, info);
}
/* Computing MAX */
r__1 = 10.f, r__2 = sqrt((real) (*n));
err_lbnd__ = f2cmax(r__1,r__2) * slamch_("Epsilon");
if (*n_err_bnds__ >= 1 && n_norms__ >= 1) {
/* Compute scaled normwise condition number cond(A*C). */
if (rcequ) {
rcond_tmp__ = sla_syrcond_(uplo, n, &a[a_offset], lda, &af[
af_offset], ldaf, &ipiv[1], &c_n1, &s[1], info, &work[1],
&iwork[1]);
} else {
rcond_tmp__ = sla_syrcond_(uplo, n, &a[a_offset], lda, &af[
af_offset], ldaf, &ipiv[1], &c__0, &s[1], info, &work[1],
&iwork[1]);
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
/* Cap the error at 1.0. */
if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1
<< 1)] > 1.f) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f;
}
/* Threshold the error (see LAWN). */
if (rcond_tmp__ < illrcond_thresh__) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f;
err_bnds_norm__[j + err_bnds_norm_dim1] = 0.f;
if (*info <= *n) {
*info = *n + j;
}
} else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] <
err_lbnd__) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__;
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f;
}
/* Save the condition number. */
if (*n_err_bnds__ >= 3) {
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__;
}
}
}
if (*n_err_bnds__ >= 1 && n_norms__ >= 2) {
/* Compute componentwise condition number cond(A*diag(Y(:,J))) for */
/* each right-hand side using the current solution as an estimate of */
/* the true solution. If the componentwise error estimate is too */
/* large, then the solution is a lousy estimate of truth and the */
/* estimated RCOND may be too optimistic. To avoid misleading users, */
/* the inverse condition number is set to 0.0 when the estimated */
/* cwise error is at least CWISE_WRONG. */
cwise_wrong__ = sqrt(slamch_("Epsilon"));
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] <
cwise_wrong__) {
rcond_tmp__ = sla_syrcond_(uplo, n, &a[a_offset], lda, &af[
af_offset], ldaf, &ipiv[1], &c__1, &x[j * x_dim1 + 1],
info, &work[1], &iwork[1]);
} else {
rcond_tmp__ = 0.f;
}
/* Cap the error at 1.0. */
if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1
<< 1)] > 1.f) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f;
}
/* Threshold the error (see LAWN). */
if (rcond_tmp__ < illrcond_thresh__) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f;
err_bnds_comp__[j + err_bnds_comp_dim1] = 0.f;
if (! ignore_cwise__ && *info < *n + j) {
*info = *n + j;
}
} else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] <
err_lbnd__) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f;
}
/* Save the condition number. */
if (*n_err_bnds__ >= 3) {
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__;
}
}
}
return;
/* End of SSYRFSX */
} /* ssyrfsx_ */
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