text: /* 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)
  */
  
  
  
  /* > \brief <b> DPOSVXX computes the solution to system of linear equations A * X = B for PO matrices</b> */
  
  /*  =========== DOCUMENTATION =========== */
  
  /* Online html documentation available at */
  /*            http://www.netlib.org/lapack/explore-html/ */
  
  /* > \htmlonly */
  /* > Download DPOSVXX + dependencies */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dposvxx
  .f"> */
  /* > [TGZ]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dposvxx
  .f"> */
  /* > [ZIP]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dposvxx
  .f"> */
  /* > [TXT]</a> */
  /* > \endhtmlonly */
  
  /*  Definition: */
  /*  =========== */
  
  /*       SUBROUTINE DPOSVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED, */
  /*                           S, B, LDB, X, LDX, RCOND, RPVGRW, BERR, */
  /*                           N_ERR_BNDS, ERR_BNDS_NORM, ERR_BNDS_COMP, */
  /*                           NPARAMS, PARAMS, WORK, IWORK, INFO ) */
  
  /*       CHARACTER          EQUED, FACT, UPLO */
  /*       INTEGER            INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS, */
  /*      $                   N_ERR_BNDS */
  /*       DOUBLE PRECISION   RCOND, RPVGRW */
  /*       INTEGER            IWORK( * ) */
  /*       DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * ), B( LDB, * ), */
  /*      $                   X( LDX, * ), WORK( * ) */
  /*       DOUBLE PRECISION   S( * ), PARAMS( * ), BERR( * ), */
  /*      $                   ERR_BNDS_NORM( NRHS, * ), */
  /*      $                   ERR_BNDS_COMP( NRHS, * ) */
  
  
  /* > \par Purpose: */
  /*  ============= */
  /* > */
  /* > \verbatim */
  /* > */
  /* >    DPOSVXX uses the Cholesky factorization A = U**T*U or A = L*L**T */
  /* >    to compute the solution to a double precision system of linear equations */
  /* >    A * X = B, where A is an N-by-N symmetric positive definite matrix */
  /* >    and X and B are N-by-NRHS matrices. */
  /* > */
  /* >    If requested, both normwise and maximum componentwise error bounds */
  /* >    are returned. DPOSVXX will return a solution with a tiny */
  /* >    guaranteed error (O(eps) where eps is the working machine */
  /* >    precision) unless the matrix is very ill-conditioned, in which */
  /* >    case a warning is returned. Relevant condition numbers also are */
  /* >    calculated and returned. */
  /* > */
  /* >    DPOSVXX accepts user-provided factorizations and equilibration */
  /* >    factors; see the definitions of the FACT and EQUED options. */
  /* >    Solving with refinement and using a factorization from a previous */
  /* >    DPOSVXX call will also produce a solution with either O(eps) */
  /* >    errors or warnings, but we cannot make that claim for general */
  /* >    user-provided factorizations and equilibration factors if they */
  /* >    differ from what DPOSVXX would itself produce. */
  /* > \endverbatim */
  
  /* > \par Description: */
  /*  ================= */
  /* > */
  /* > \verbatim */
  /* > */
  /* >    The following steps are performed: */
  /* > */
  /* >    1. If FACT = 'E', double precision scaling factors are computed to equilibrate */
  /* >    the system: */
  /* > */
  /* >      diag(S)*A*diag(S)     *inv(diag(S))*X = diag(S)*B */
  /* > */
  /* >    Whether or not the system will be equilibrated depends on the */
  /* >    scaling of the matrix A, but if equilibration is used, A is */
  /* >    overwritten by diag(S)*A*diag(S) and B by diag(S)*B. */
  /* > */
  /* >    2. If FACT = 'N' or 'E', the Cholesky decomposition is used to */
  /* >    factor the matrix A (after equilibration if FACT = 'E') as */
  /* >       A = U**T* U,  if UPLO = 'U', or */
  /* >       A = L * L**T,  if UPLO = 'L', */
  /* >    where U is an upper triangular matrix and L is a lower triangular */
  /* >    matrix. */
  /* > */
  /* >    3. If the leading i-by-i principal minor is not positive definite, */
  /* >    then the routine returns with INFO = i. Otherwise, the factored */
  /* >    form of A is used to estimate the condition number of the matrix */
  /* >    A (see argument RCOND).  If the reciprocal of the condition number */
  /* >    is less than machine precision, the routine still goes on to solve */
  /* >    for X and compute error bounds as described below. */
  /* > */
  /* >    4. The system of equations is solved for X using the factored form */
  /* >    of A. */
  /* > */
  /* >    5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero), */
  /* >    the routine will use iterative refinement to try to get a small */
  /* >    error and error bounds.  Refinement calculates the residual to at */
  /* >    least twice the working precision. */
  /* > */
  /* >    6. If equilibration was used, the matrix X is premultiplied by */
  /* >    diag(S) so that it solves the original system before */
  /* >    equilibration. */
  /* > \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] FACT */
  /* > \verbatim */
  /* >          FACT is CHARACTER*1 */
  /* >     Specifies whether or not the factored form of the matrix A is */
  /* >     supplied on entry, and if not, whether the matrix A should be */
  /* >     equilibrated before it is factored. */
  /* >       = 'F':  On entry, AF contains the factored form of A. */
  /* >               If EQUED is not 'N', the matrix A has been */
  /* >               equilibrated with scaling factors given by S. */
  /* >               A and AF are not modified. */
  /* >       = 'N':  The matrix A will be copied to AF and factored. */
  /* >       = 'E':  The matrix A will be equilibrated if necessary, then */
  /* >               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,out] A */
  /* > \verbatim */
  /* >          A is DOUBLE PRECISION array, dimension (LDA,N) */
  /* >     On entry, the symmetric matrix A, except if FACT = 'F' and EQUED = */
  /* >     'Y', then A must contain the equilibrated matrix */
  /* >     diag(S)*A*diag(S).  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.  A is */
  /* >     not modified if FACT = 'F' or 'N', or if FACT = 'E' and EQUED = */
  /* >     'N' on exit. */
  /* > */
  /* >     On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by */
  /* >     diag(S)*A*diag(S). */
  /* > \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 triangular factor U or L from the Cholesky */
  /* >     factorization A = U**T*U or A = L*L**T, in the same storage */
  /* >     format as A.  If EQUED .ne. 'N', then AF is the factored */
  /* >     form of the equilibrated matrix diag(S)*A*diag(S). */
  /* > */
  /* >     If FACT = 'N', then AF is an output argument and on exit */
  /* >     returns the triangular factor U or L from the Cholesky */
  /* >     factorization A = U**T*U or A = L*L**T of the original */
  /* >     matrix A. */
  /* > */
  /* >     If FACT = 'E', then AF is an output argument and on exit */
  /* >     returns the triangular factor U or L from the Cholesky */
  /* >     factorization A = U**T*U or A = L*L**T of the equilibrated */
  /* >     matrix A (see the description of A for the form of the */
  /* >     equilibrated matrix). */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LDAF */
  /* > \verbatim */
  /* >          LDAF is INTEGER */
  /* >     The leading dimension of the array AF.  LDAF >= f2cmax(1,N). */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] EQUED */
  /* > \verbatim */
  /* >          EQUED is CHARACTER*1 */
  /* >     Specifies the form of equilibration that was done. */
  /* >       = 'N':  No equilibration (always true if FACT = 'N'). */
  /* >       = 'Y':  Both row and column equilibration, i.e., A has been */
  /* >               replaced by diag(S) * A * diag(S). */
  /* >     EQUED is an input argument if FACT = 'F'; otherwise, it is an */
  /* >     output argument. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] S */
  /* > \verbatim */
  /* >          S is DOUBLE PRECISION array, dimension (N) */
  /* >     The row 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,out] B */
  /* > \verbatim */
  /* >          B is DOUBLE PRECISION array, dimension (LDB,NRHS) */
  /* >     On entry, the N-by-NRHS right hand side matrix B. */
  /* >     On exit, */
  /* >     if EQUED = 'N', B is not modified; */
  /* >     if EQUED = 'Y', B is overwritten by diag(S)*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, the N-by-NRHS solution matrix X to the original */
  /* >     system of equations.  Note that A and B are modified on exit if */
  /* >     EQUED .ne. 'N', and the solution to the equilibrated system is */
  /* >     inv(diag(S))*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 */
  /* >     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] RPVGRW */
  /* > \verbatim */
  /* >          RPVGRW is DOUBLE PRECISION */
  /* >     Reciprocal pivot growth.  On exit, this contains the reciprocal */
  /* >     pivot growth factor norm(A)/norm(U). The "f2cmax absolute element" */
  /* >     norm is used.  If this is much less than 1, then the stability of */
  /* >     the LU factorization of the (equilibrated) matrix A could be poor. */
  /* >     This also means that the solution X, estimated condition numbers, */
  /* >     and error bounds could be unreliable. If factorization fails with */
  /* >     0<INFO<=N, then this contains the reciprocal pivot growth factor */
  /* >     for the leading INFO columns of A. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] BERR */
  /* > \verbatim */
  /* >          BERR is DOUBLE PRECISION array, dimension (NRHS) */
  /* >     Componentwise relative backward error.  This is the */
  /* >     componentwise relative backward error of each solution vector X(j) */
  /* >     (i.e., the smallest relative change in any element of A or B that */
  /* >     makes X(j) an exact solution). */
  /* > \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 DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
  /* >     For each right-hand side, this array contains information about */
  /* >     various error bounds and condition numbers corresponding to the */
  /* >     normwise relative error, which is defined as follows: */
  /* > */
  /* >     Normwise relative error in the ith solution vector: */
  /* >             max_j (abs(XTRUE(j,i) - X(j,i))) */
  /* >            ------------------------------ */
  /* >                  max_j abs(X(j,i)) */
  /* > */
  /* >     The array is indexed by the type of error information as described */
  /* >     below. There currently are up to three pieces of information */
  /* >     returned. */
  /* > */
  /* >     The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */
  /* >     right-hand side. */
  /* > */
  /* >     The second index in ERR_BNDS_NORM(:,err) contains the following */
  /* >     three fields: */
  /* >     err = 1 "Trust/don't trust" boolean. Trust the answer if the */
  /* >              reciprocal condition number is less than the threshold */
  /* >              sqrt(n) * dlamch('Epsilon'). */
  /* > */
  /* >     err = 2 "Guaranteed" error bound: The estimated forward error, */
  /* >              almost certainly within a factor of 10 of the true error */
  /* >              so long as the next entry is greater than the threshold */
  /* >              sqrt(n) * dlamch('Epsilon'). This error bound should only */
  /* >              be trusted if the previous boolean is true. */
  /* > */
  /* >     err = 3  Reciprocal condition number: Estimated normwise */
  /* >              reciprocal condition number.  Compared with the threshold */
  /* >              sqrt(n) * dlamch('Epsilon') to determine if the error */
  /* >              estimate is "guaranteed". These reciprocal condition */
  /* >              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
  /* >              appropriately scaled matrix Z. */
  /* >              Let Z = S*A, where S scales each row by a power of the */
  /* >              radix so all absolute row sums of Z are approximately 1. */
  /* > */
  /* >     See Lapack Working Note 165 for further details and extra */
  /* >     cautions. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] ERR_BNDS_COMP */
  /* > \verbatim */
  /* >          ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
  /* >     For each right-hand side, this array contains information about */
  /* >     various error bounds and condition numbers corresponding to the */
  /* >     componentwise relative error, which is defined as follows: */
  /* > */
  /* >     Componentwise relative error in the ith solution vector: */
  /* >                    abs(XTRUE(j,i) - X(j,i)) */
  /* >             max_j ---------------------- */
  /* >                         abs(X(j,i)) */
  /* > */
  /* >     The array is indexed by the right-hand side i (on which the */
  /* >     componentwise relative error depends), and the type of error */
  /* >     information as described below. There currently are up to three */
  /* >     pieces of information returned for each right-hand side. If */
  /* >     componentwise accuracy is not requested (PARAMS(3) = 0.0), then */
  /* >     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most */
  /* >     the first (:,N_ERR_BNDS) entries are returned. */
  /* > */
  /* >     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */
  /* >     right-hand side. */
  /* > */
  /* >     The second index in ERR_BNDS_COMP(:,err) contains the following */
  /* >     three fields: */
  /* >     err = 1 "Trust/don't trust" boolean. Trust the answer if the */
  /* >              reciprocal condition number is less than the threshold */
  /* >              sqrt(n) * dlamch('Epsilon'). */
  /* > */
  /* >     err = 2 "Guaranteed" error bound: The estimated forward error, */
  /* >              almost certainly within a factor of 10 of the true error */
  /* >              so long as the next entry is greater than the threshold */
  /* >              sqrt(n) * dlamch('Epsilon'). This error bound should only */
  /* >              be trusted if the previous boolean is true. */
  /* > */
  /* >     err = 3  Reciprocal condition number: Estimated componentwise */
  /* >              reciprocal condition number.  Compared with the threshold */
  /* >              sqrt(n) * dlamch('Epsilon') to determine if the error */
  /* >              estimate is "guaranteed". These reciprocal condition */
  /* >              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
  /* >              appropriately scaled matrix Z. */
  /* >              Let Z = S*(A*diag(x)), where x is the solution for the */
  /* >              current right-hand side and S scales each row of */
  /* >              A*diag(x) by a power of the radix so all absolute row */
  /* >              sums of Z are approximately 1. */
  /* > */
  /* >     See Lapack Working Note 165 for further details and extra */
  /* >     cautions. */
  /* > \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 DOUBLE PRECISION 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: 1.0D+0 */
  /* >            = 0.0:  No refinement is performed, and no error bounds are */
  /* >                    computed. */
  /* >            = 1.0:  Use the extra-precise refinement algorithm. */
  /* >              (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 DOUBLE PRECISION 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 doublePOsolve */
  
  /*  ===================================================================== */
  /* Subroutine */ int dposvxx_(char *fact, char *uplo, integer *n, integer *
  	nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, 
  	char *equed, doublereal *s, doublereal *b, integer *ldb, doublereal *
  	x, integer *ldx, doublereal *rcond, doublereal *rpvgrw, doublereal *
  	berr, integer *n_err_bnds__, doublereal *err_bnds_norm__, doublereal *
  	err_bnds_comp__, integer *nparams, doublereal *params, doublereal *
  	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;
      doublereal d__1, d__2;
  
      /* Local variables */
      doublereal amax, smin, smax;
      extern doublereal dla_porpvgrw_(char *, integer *, doublereal *, integer 
  	    *, doublereal *, integer *, doublereal *);
      integer j;
      extern logical lsame_(char *, char *);
      doublereal scond;
      logical equil, rcequ;
      extern doublereal dlamch_(char *);
      logical nofact;
      extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
  	    doublereal *, integer *, doublereal *, integer *), 
  	    xerbla_(char *, integer *, ftnlen);
      doublereal bignum;
      integer infequ;
      extern /* Subroutine */ int dlaqsy_(char *, integer *, doublereal *, 
  	    integer *, doublereal *, doublereal *, doublereal *, char *), dpotrf_(char *, integer *, doublereal *, integer 
  	    *, integer *);
      doublereal smlnum;
      extern /* Subroutine */ int dpotrs_(char *, integer *, integer *, 
  	    doublereal *, integer *, doublereal *, integer *, integer *), dlascl2_(integer *, integer *, doublereal *, doublereal *
  	    , integer *), dpoequb_(integer *, doublereal *, integer *, 
  	    doublereal *, doublereal *, doublereal *, integer *), dporfsx_(
  	    char *, char *, integer *, integer *, doublereal *, integer *, 
  	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
  	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
  	    doublereal *, doublereal *, integer *, doublereal *, 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 */
  
  
  /*  ================================================================== */
  
  
      /* 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;
      --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;
      nofact = lsame_(fact, "N");
      equil = lsame_(fact, "E");
      smlnum = dlamch_("Safe minimum");
      bignum = 1. / smlnum;
      if (nofact || equil) {
  	*(unsigned char *)equed = 'N';
  	rcequ = FALSE_;
      } else {
  	rcequ = lsame_(equed, "Y");
      }
  
  /*     Default is failure.  If an input parameter is wrong or */
  /*     factorization fails, make everything look horrible.  Only the */
  /*     pivot growth is set here, the rest is initialized in DPORFSX. */
  
      *rpvgrw = 0.;
  
  /*     Test the input parameters.  PARAMS is not tested until DPORFSX. */
  
      if (! nofact && ! equil && ! 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 (lsame_(fact, "F") && ! (rcequ || lsame_(
  	    equed, "N"))) {
  	*info = -9;
      } else {
  	if (rcequ) {
  	    smin = bignum;
  	    smax = 0.;
  	    i__1 = *n;
  	    for (j = 1; j <= i__1; ++j) {
  /* Computing MIN */
  		d__1 = smin, d__2 = s[j];
  		smin = f2cmin(d__1,d__2);
  /* Computing MAX */
  		d__1 = smax, d__2 = s[j];
  		smax = f2cmax(d__1,d__2);
  /* L10: */
  	    }
  	    if (smin <= 0.) {
  		*info = -10;
  	    } else if (*n > 0) {
  		scond = f2cmax(smin,smlnum) / f2cmin(smax,bignum);
  	    } else {
  		scond = 1.;
  	    }
  	}
  	if (*info == 0) {
  	    if (*ldb < f2cmax(1,*n)) {
  		*info = -12;
  	    } else if (*ldx < f2cmax(1,*n)) {
  		*info = -14;
  	    }
  	}
      }
  
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("DPOSVXX", &i__1, (ftnlen)7);
  	return 0;
      }
  
      if (equil) {
  
  /*     Compute row and column scalings to equilibrate the matrix A. */
  
  	dpoequb_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ);
  	if (infequ == 0) {
  
  /*     Equilibrate the matrix. */
  
  	    dlaqsy_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed);
  	    rcequ = lsame_(equed, "Y");
  	}
      }
  
  /*     Scale the right-hand side. */
  
      if (rcequ) {
  	dlascl2_(n, nrhs, &s[1], &b[b_offset], ldb);
      }
  
      if (nofact || equil) {
  
  /*        Compute the Cholesky factorization of A. */
  
  	dlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
  	dpotrf_(uplo, n, &af[af_offset], ldaf, info);
  
  /*        Return if INFO is non-zero. */
  
  	if (*info != 0) {
  
  /*           Pivot in column INFO is exactly 0 */
  /*           Compute the reciprocal pivot growth factor of the */
  /*           leading rank-deficient INFO columns of A. */
  
  	    *rpvgrw = dla_porpvgrw_(uplo, info, &a[a_offset], lda, &af[
  		    af_offset], ldaf, &work[1]);
  	    return 0;
  	}
      }
  
  /*     Compute the reciprocal growth factor RPVGRW. */
  
      *rpvgrw = dla_porpvgrw_(uplo, n, &a[a_offset], lda, &af[af_offset], ldaf,
  	     &work[1]);
  
  /*     Compute the solution matrix X. */
  
      dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
      dpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info);
  
  /*     Use iterative refinement to improve the computed solution and */
  /*     compute error bounds and backward error estimates for it. */
  
      dporfsx_(uplo, equed, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &
  	    s[1], &b[b_offset], ldb, &x[x_offset], ldx, rcond, &berr[1], 
  	    n_err_bnds__, &err_bnds_norm__[err_bnds_norm_offset], &
  	    err_bnds_comp__[err_bnds_comp_offset], nparams, &params[1], &work[
  	    1], &iwork[1], info);
  
  /*     Scale solutions. */
  
      if (rcequ) {
  	dlascl2_(n, nrhs, &s[1], &x[x_offset], ldx);
      }
  
      return 0;
  
  /*     End of DPOSVXX */
  
  } /* dposvxx_ */
  
  