OpenBLAS/lapack-netlib/SRC/dsysvx.c

/* 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 int logical;
typedef short int shortlogical;
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++ */

#define F2C_proc_par_types 1
#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__1 = 1;
static integer c_n1 = -1;

/* > \brief <b> DSYSVX computes the solution to system of linear equations A * X = B for SY matrices</b> */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download DSYSVX + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsysvx.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsysvx.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsysvx.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE DSYSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, */
/*                          LDB, X, LDX, RCOND, FERR, BERR, WORK, LWORK, */
/*                          IWORK, INFO ) */

/*       CHARACTER          FACT, UPLO */
/*       INTEGER            INFO, LDA, LDAF, LDB, LDX, LWORK, N, NRHS */
/*       DOUBLE PRECISION   RCOND */
/*       INTEGER            IPIV( * ), IWORK( * ) */
/*       DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * ), B( LDB, * ), */
/*      $                   BERR( * ), FERR( * ), WORK( * ), X( LDX, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DSYSVX uses the diagonal pivoting factorization to compute the */
/* > solution to a real 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. */
/* > \endverbatim */

/* > \par Description: */
/*  ================= */
/* > */
/* > \verbatim */
/* > */
/* > 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. */
/* > \endverbatim */

/*  Arguments: */
/*  ========== */

/* > \param[in] FACT */
/* > \verbatim */
/* >          FACT is 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.  AF and IPIV will not be modified. */
/* >          = 'N':  The matrix A will be copied to AF and factored. */
/* > \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] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The number of linear equations, i.e., 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 DOUBLE PRECISION 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,out] AF */
/* > \verbatim */
/* >          AF is DOUBLE PRECISION 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 DSYTRF. */
/* > */
/* >          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. */
/* > \endverbatim */
/* > */
/* > \param[in] LDAF */
/* > \verbatim */
/* >          LDAF is INTEGER */
/* >          The leading dimension of the array AF.  LDAF >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] IPIV */
/* > \verbatim */
/* >          IPIV is 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 DSYTRF. */
/* >          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 DSYTRF. */
/* > \endverbatim */
/* > */
/* > \param[in] B */
/* > \verbatim */
/* >          B is DOUBLE PRECISION array, dimension (LDB,NRHS) */
/* >          The N-by-NRHS 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[out] X */
/* > \verbatim */
/* >          X is DOUBLE PRECISION array, dimension (LDX,NRHS) */
/* >          If INFO = 0 or INFO = N+1, the N-by-NRHS 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 DOUBLE PRECISION */
/* >          The estimate of the reciprocal condition number of the matrix */
/* >          A.  If RCOND is less than the machine precision (in */
/* >          particular, if RCOND = 0), the matrix is singular to working */
/* >          precision.  This condition is indicated by a return code of */
/* >          INFO > 0. */
/* > \endverbatim */
/* > */
/* > \param[out] FERR */
/* > \verbatim */
/* >          FERR is DOUBLE PRECISION array, dimension (NRHS) */
/* >          The estimated forward error bound for each solution vector */
/* >          X(j) (the j-th column of the solution matrix X). */
/* >          If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* >          is an estimated upper bound for the magnitude of the largest */
/* >          element in (X(j) - XTRUE) divided by the magnitude of the */
/* >          largest element in X(j).  The estimate is as reliable as */
/* >          the estimate for RCOND, and is almost always a slight */
/* >          overestimate of the true error. */
/* > \endverbatim */
/* > */
/* > \param[out] BERR */
/* > \verbatim */
/* >          BERR is DOUBLE PRECISION array, dimension (NRHS) */
/* >          The componentwise relative backward error of each solution */
/* >          vector X(j) (i.e., the smallest relative change in */
/* >          any element of A or B that makes X(j) an exact solution). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* >          LWORK is INTEGER */
/* >          The length of WORK.  LWORK >= f2cmax(1,3*N), and for best */
/* >          performance, when FACT = 'N', LWORK >= f2cmax(1,3*N,N*NB), where */
/* >          NB is the optimal blocksize for DSYTRF. */
/* > */
/* >          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. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is 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. */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \date April 2012 */

/* > \ingroup doubleSYsolve */

/*  ===================================================================== */
/* Subroutine */ int dsysvx_(char *fact, char *uplo, integer *n, integer *
	nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, 
	integer *ipiv, doublereal *b, integer *ldb, doublereal *x, integer *
	ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, 
	doublereal *work, integer *lwork, integer *iwork, 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 */
    extern logical lsame_(char *, char *);
    doublereal anorm;
    integer nb;
    extern doublereal dlamch_(char *);
    logical nofact;
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *), 
	    xerbla_(char *, integer *, ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern doublereal dlansy_(char *, char *, integer *, doublereal *, 
	    integer *, doublereal *);
    extern /* Subroutine */ int dsycon_(char *, integer *, doublereal *, 
	    integer *, integer *, doublereal *, doublereal *, doublereal *, 
	    integer *, integer *), dsyrfs_(char *, integer *, integer 
	    *, doublereal *, integer *, doublereal *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
	    doublereal *, doublereal *, integer *, integer *), 
	    dsytrf_(char *, integer *, doublereal *, integer *, integer *, 
	    doublereal *, integer *, integer *);
    integer lwkopt;
    logical lquery;
    extern /* Subroutine */ int dsytrs_(char *, integer *, integer *, 
	    doublereal *, integer *, integer *, doublereal *, integer *, 
	    integer *);


/*  -- LAPACK driver 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 */


/*  ===================================================================== */


/*     Test the input parameters. */

    /* Parameter adjustments */
    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;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1 * 1;
    x -= x_offset;
    --ferr;
    --berr;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;
    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 < f2cmax(1,*n)) {
	*info = -6;
    } else if (*ldaf < f2cmax(1,*n)) {
	*info = -8;
    } else if (*ldb < f2cmax(1,*n)) {
	*info = -11;
    } else if (*ldx < f2cmax(1,*n)) {
	*info = -13;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = 1, i__2 = *n * 3;
	if (*lwork < f2cmax(i__1,i__2) && ! lquery) {
	    *info = -18;
	}
    }

    if (*info == 0) {
/* Computing MAX */
	i__1 = 1, i__2 = *n * 3;
	lwkopt = f2cmax(i__1,i__2);
	if (nofact) {
	    nb = ilaenv_(&c__1, "DSYTRF", uplo, n, &c_n1, &c_n1, &c_n1, (
		    ftnlen)6, (ftnlen)1);
/* Computing MAX */
	    i__1 = lwkopt, i__2 = *n * nb;
	    lwkopt = f2cmax(i__1,i__2);
	}
	work[1] = (doublereal) lwkopt;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DSYSVX", &i__1, (ftnlen)6);
	return 0;
    } else if (lquery) {
	return 0;
    }

    if (nofact) {

/*        Compute the factorization A = U*D*U**T or A = L*D*L**T. */

	dlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
	dsytrf_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &work[1], lwork, 
		info);

/*        Return if INFO is non-zero. */

	if (*info > 0) {
	    *rcond = 0.;
	    return 0;
	}
    }

/*     Compute the norm of the matrix A. */

    anorm = dlansy_("I", uplo, n, &a[a_offset], lda, &work[1]);

/*     Compute the reciprocal of the condition number of A. */

    dsycon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1], 
	    &iwork[1], info);

/*     Compute the solution vectors X. */

    dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    dsytrs_(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. */

    dsyrfs_(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]
	    , &iwork[1], info);

/*     Set INFO = N+1 if the matrix is singular to working precision. */

    if (*rcond < dlamch_("Epsilon")) {
	*info = *n + 1;
    }

    work[1] = (doublereal) lwkopt;

    return 0;

/*     End of DSYSVX */

} /* dsysvx_ */