text: #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;
  #ifdef _MSC_VER
  static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
  static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
  static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
  static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
  #else
  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;}
  #endif
  #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)); }
  #ifdef _MSC_VER
  #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
  #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/Cd(b)._Val[1]);}
  #else
  #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  #endif
  #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) = conjf(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) (cimagf(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;
  }
  #ifdef _MSC_VER
  static _Fcomplex cpow_ui(complex x, integer n) {
  	complex pow={1.0,0.0}; unsigned long int u;
  		if(n != 0) {
  		if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
  		for(u = n; ; ) {
  			if(u & 01) pow.r *= x.r, pow.i *= x.i;
  			if(u >>= 1) x.r *= x.r, x.i *= x.i;
  			else break;
  		}
  	}
  	_Fcomplex p={pow.r, pow.i};
  	return p;
  }
  #else
  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;
  }
  #endif
  #ifdef _MSC_VER
  static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
  	_Dcomplex pow={1.0,0.0}; unsigned long int u;
  	if(n != 0) {
  		if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
  		for(u = n; ; ) {
  			if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
  			if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
  			else break;
  		}
  	}
  	_Dcomplex p = {pow._Val[0], pow._Val[1]};
  	return p;
  }
  #else
  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;
  }
  #endif
  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;
  #ifdef _MSC_VER
  	_Fcomplex zdotc = {0.0, 0.0};
  	if (incx == 1 && incy == 1) {
  		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  			zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
  			zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
  		}
  	} else {
  		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  			zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
  			zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
  		}
  	}
  	pCf(z) = zdotc;
  }
  #else
  	_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;
  }
  #endif
  static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  	integer n = *n_, incx = *incx_, incy = *incy_, i;
  #ifdef _MSC_VER
  	_Dcomplex zdotc = {0.0, 0.0};
  	if (incx == 1 && incy == 1) {
  		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  			zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
  			zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
  		}
  	} else {
  		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  			zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
  			zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
  		}
  	}
  	pCd(z) = zdotc;
  }
  #else
  	_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;
  }
  #endif	
  static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  	integer n = *n_, incx = *incx_, incy = *incy_, i;
  #ifdef _MSC_VER
  	_Fcomplex zdotc = {0.0, 0.0};
  	if (incx == 1 && incy == 1) {
  		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  			zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
  			zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
  		}
  	} else {
  		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  			zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
  			zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
  		}
  	}
  	pCf(z) = zdotc;
  }
  #else
  	_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;
  }
  #endif
  static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  	integer n = *n_, incx = *incx_, incy = *incy_, i;
  #ifdef _MSC_VER
  	_Dcomplex zdotc = {0.0, 0.0};
  	if (incx == 1 && incy == 1) {
  		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  			zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
  			zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
  		}
  	} else {
  		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  			zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
  			zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
  		}
  	}
  	pCd(z) = zdotc;
  }
  #else
  	_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;
  
  /* > \brief <b> ZPPSVX computes the solution to system of linear equations A * X = B for OTHER matrices</b> */
  
  /*  =========== DOCUMENTATION =========== */
  
  /* Online html documentation available at */
  /*            http://www.netlib.org/lapack/explore-html/ */
  
  /* > \htmlonly */
  /* > Download ZPPSVX + dependencies */
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  f"> */
  /* > [TGZ]</a> */
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  f"> */
  /* > [ZIP]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zppsvx.
  f"> */
  /* > [TXT]</a> */
  /* > \endhtmlonly */
  
  /*  Definition: */
  /*  =========== */
  
  /*       SUBROUTINE ZPPSVX( FACT, UPLO, N, NRHS, AP, AFP, EQUED, S, B, LDB, */
  /*                          X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO ) */
  
  /*       CHARACTER          EQUED, FACT, UPLO */
  /*       INTEGER            INFO, LDB, LDX, N, NRHS */
  /*       DOUBLE PRECISION   RCOND */
  /*       DOUBLE PRECISION   BERR( * ), FERR( * ), RWORK( * ), S( * ) */
  /*       COMPLEX*16         AFP( * ), AP( * ), B( LDB, * ), WORK( * ), */
  /*      $                   X( LDX, * ) */
  
  
  /* > \par Purpose: */
  /*  ============= */
  /* > */
  /* > \verbatim */
  /* > */
  /* > ZPPSVX uses the Cholesky factorization A = U**H * U or A = L * L**H to */
  /* > compute the solution to a complex system of linear equations */
  /* >    A * X = B, */
  /* > where A is an N-by-N Hermitian positive definite matrix stored in */
  /* > packed format 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 = 'E', real 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**H * U ,  if UPLO = 'U', or */
  /* >       A = L * L**H,  if UPLO = 'L', */
  /* >    where U is an upper triangular matrix, L is a lower triangular */
  /* >    matrix, and **H indicates conjugate transpose. */
  /* > */
  /* > 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.  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. */
  /* > */
  /* > 4. The system of equations is solved for X using the factored form */
  /* >    of A. */
  /* > */
  /* > 5. Iterative refinement is applied to improve the computed solution */
  /* >    matrix and calculate error bounds and backward error estimates */
  /* >    for it. */
  /* > */
  /* > 6. If equilibration was used, the matrix X is premultiplied by */
  /* >    diag(S) so that it solves the original system before */
  /* >    equilibration. */
  /* > \endverbatim */
  
  /*  Arguments: */
  /*  ========== */
  
  /* > \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, AFP contains the factored form of A. */
  /* >                  If EQUED = 'Y', the matrix A has been equilibrated */
  /* >                  with scaling factors given by S.  AP and AFP will not */
  /* >                  be modified. */
  /* >          = 'N':  The matrix A will be copied to AFP and factored. */
  /* >          = 'E':  The matrix A will be equilibrated if necessary, then */
  /* >                  copied to AFP 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] AP */
  /* > \verbatim */
  /* >          AP is COMPLEX*16 array, dimension (N*(N+1)/2) */
  /* >          On entry, the upper or lower triangle of the Hermitian matrix */
  /* >          A, packed columnwise in a linear array, except if FACT = 'F' */
  /* >          and EQUED = 'Y', then A must contain the equilibrated matrix */
  /* >          diag(S)*A*diag(S).  The j-th column of A is stored in the */
  /* >          array AP as follows: */
  /* >          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
  /* >          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
  /* >          See below for further details.  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,out] AFP */
  /* > \verbatim */
  /* >          AFP is COMPLEX*16 array, dimension (N*(N+1)/2) */
  /* >          If FACT = 'F', then AFP is an input argument and on entry */
  /* >          contains the triangular factor U or L from the Cholesky */
  /* >          factorization A = U**H*U or A = L*L**H, in the same storage */
  /* >          format as A.  If EQUED .ne. 'N', then AFP is the factored */
  /* >          form of the equilibrated matrix A. */
  /* > */
  /* >          If FACT = 'N', then AFP is an output argument and on exit */
  /* >          returns the triangular factor U or L from the Cholesky */
  /* >          factorization A = U**H * U or A = L * L**H of the original */
  /* >          matrix A. */
  /* > */
  /* >          If FACT = 'E', then AFP is an output argument and on exit */
  /* >          returns the triangular factor U or L from the Cholesky */
  /* >          factorization A = U**H * U or A = L * L**H of the equilibrated */
  /* >          matrix A (see the description of AP for the form of the */
  /* >          equilibrated matrix). */
  /* > \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':  Equilibration was done, 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 scale factors for A; not accessed if EQUED = 'N'.  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. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] B */
  /* > \verbatim */
  /* >          B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS) */
  /* >          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X to */
  /* >          the original system of equations.  Note that if EQUED = 'Y', */
  /* >          A and B are modified on exit, 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 */
  /* >          The estimate of the reciprocal condition number of the matrix */
  /* >          A after equilibration (if done).  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 COMPLEX*16 array, dimension (2*N) */
  /* > \endverbatim */
  /* > */
  /* > \param[out] RWORK */
  /* > \verbatim */
  /* >          RWORK is DOUBLE PRECISION 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:  the leading minor of order i of A is */
  /* >                       not positive definite, so the factorization */
  /* >                       could not be completed, and the solution has not */
  /* >                       been computed. RCOND = 0 is returned. */
  /* >                = N+1: U 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 complex16OTHERsolve */
  
  /* > \par Further Details: */
  /*  ===================== */
  /* > */
  /* > \verbatim */
  /* > */
  /* >  The packed storage scheme is illustrated by the following example */
  /* >  when N = 4, UPLO = 'U': */
  /* > */
  /* >  Two-dimensional storage of the Hermitian matrix A: */
  /* > */
  /* >     a11 a12 a13 a14 */
  /* >         a22 a23 a24 */
  /* >             a33 a34     (aij = conjg(aji)) */
  /* >                 a44 */
  /* > */
  /* >  Packed storage of the upper triangle of A: */
  /* > */
  /* >  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] */
  /* > \endverbatim */
  /* > */
  /*  ===================================================================== */
  /* Subroutine */ int zppsvx_(char *fact, char *uplo, integer *n, integer *
  	nrhs, doublecomplex *ap, doublecomplex *afp, char *equed, doublereal *
  	s, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, 
  	doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *
  	work, doublereal *rwork, integer *info)
  {
      /* System generated locals */
      integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
      doublereal d__1, d__2;
      doublecomplex z__1;
  
      /* Local variables */
      doublereal amax, smin, smax;
      integer i__, j;
      extern logical lsame_(char *, char *);
      doublereal scond, anorm;
      logical equil, rcequ;
      extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
  	    doublecomplex *, integer *);
      extern doublereal dlamch_(char *);
      logical nofact;
      extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
      doublereal bignum;
      integer infequ;
      extern doublereal zlanhp_(char *, char *, integer *, doublecomplex *, 
  	    doublereal *);
      extern /* Subroutine */ int zlaqhp_(char *, integer *, doublecomplex *, 
  	    doublereal *, doublereal *, doublereal *, char *),
  	     zlacpy_(char *, integer *, integer *, doublecomplex *, integer *,
  	     doublecomplex *, integer *), zppcon_(char *, integer *, 
  	    doublecomplex *, doublereal *, doublereal *, doublecomplex *, 
  	    doublereal *, integer *);
      doublereal smlnum;
      extern /* Subroutine */ int zppequ_(char *, integer *, doublecomplex *, 
  	    doublereal *, doublereal *, doublereal *, integer *), 
  	    zpprfs_(char *, integer *, integer *, doublecomplex *, 
  	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
  	    integer *, doublereal *, doublereal *, doublecomplex *, 
  	    doublereal *, integer *), zpptrf_(char *, integer *, 
  	    doublecomplex *, integer *), zpptrs_(char *, integer *, 
  	    integer *, doublecomplex *, doublecomplex *, 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 */
      --ap;
      --afp;
      --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;
      --ferr;
      --berr;
      --work;
      --rwork;
  
      /* Function Body */
      *info = 0;
      nofact = lsame_(fact, "N");
      equil = lsame_(fact, "E");
      if (nofact || equil) {
  	*(unsigned char *)equed = 'N';
  	rcequ = FALSE_;
      } else {
  	rcequ = lsame_(equed, "Y");
  	smlnum = dlamch_("Safe minimum");
  	bignum = 1. / smlnum;
      }
  
  /*     Test the input parameters. */
  
      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 (lsame_(fact, "F") && ! (rcequ || lsame_(
  	    equed, "N"))) {
  	*info = -7;
      } 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 = -8;
  	    } else if (*n > 0) {
  		scond = f2cmax(smin,smlnum) / f2cmin(smax,bignum);
  	    } else {
  		scond = 1.;
  	    }
  	}
  	if (*info == 0) {
  	    if (*ldb < f2cmax(1,*n)) {
  		*info = -10;
  	    } else if (*ldx < f2cmax(1,*n)) {
  		*info = -12;
  	    }
  	}
      }
  
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("ZPPSVX", &i__1, (ftnlen)6);
  	return 0;
      }
  
      if (equil) {
  
  /*        Compute row and column scalings to equilibrate the matrix A. */
  
  	zppequ_(uplo, n, &ap[1], &s[1], &scond, &amax, &infequ);
  	if (infequ == 0) {
  
  /*           Equilibrate the matrix. */
  
  	    zlaqhp_(uplo, n, &ap[1], &s[1], &scond, &amax, equed);
  	    rcequ = lsame_(equed, "Y");
  	}
      }
  
  /*     Scale the right-hand side. */
  
      if (rcequ) {
  	i__1 = *nrhs;
  	for (j = 1; j <= i__1; ++j) {
  	    i__2 = *n;
  	    for (i__ = 1; i__ <= i__2; ++i__) {
  		i__3 = i__ + j * b_dim1;
  		i__4 = i__;
  		i__5 = i__ + j * b_dim1;
  		z__1.r = s[i__4] * b[i__5].r, z__1.i = s[i__4] * b[i__5].i;
  		b[i__3].r = z__1.r, b[i__3].i = z__1.i;
  /* L20: */
  	    }
  /* L30: */
  	}
      }
  
      if (nofact || equil) {
  
  /*        Compute the Cholesky factorization A = U**H * U or A = L * L**H. */
  
  	i__1 = *n * (*n + 1) / 2;
  	zcopy_(&i__1, &ap[1], &c__1, &afp[1], &c__1);
  	zpptrf_(uplo, n, &afp[1], info);
  
  /*        Return if INFO is non-zero. */
  
  	if (*info > 0) {
  	    *rcond = 0.;
  	    return 0;
  	}
      }
  
  /*     Compute the norm of the matrix A. */
  
      anorm = zlanhp_("I", uplo, n, &ap[1], &rwork[1]);
  
  /*     Compute the reciprocal of the condition number of A. */
  
      zppcon_(uplo, n, &afp[1], &anorm, rcond, &work[1], &rwork[1], info);
  
  /*     Compute the solution matrix X. */
  
      zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
      zpptrs_(uplo, n, nrhs, &afp[1], &x[x_offset], ldx, info);
  
  /*     Use iterative refinement to improve the computed solution and */
  /*     compute error bounds and backward error estimates for it. */
  
      zpprfs_(uplo, n, nrhs, &ap[1], &afp[1], &b[b_offset], ldb, &x[x_offset], 
  	    ldx, &ferr[1], &berr[1], &work[1], &rwork[1], info);
  
  /*     Transform the solution matrix X to a solution of the original */
  /*     system. */
  
      if (rcequ) {
  	i__1 = *nrhs;
  	for (j = 1; j <= i__1; ++j) {
  	    i__2 = *n;
  	    for (i__ = 1; i__ <= i__2; ++i__) {
  		i__3 = i__ + j * x_dim1;
  		i__4 = i__;
  		i__5 = i__ + j * x_dim1;
  		z__1.r = s[i__4] * x[i__5].r, z__1.i = s[i__4] * x[i__5].i;
  		x[i__3].r = z__1.r, x[i__3].i = z__1.i;
  /* L40: */
  	    }
  /* L50: */
  	}
  	i__1 = *nrhs;
  	for (j = 1; j <= i__1; ++j) {
  	    ferr[j] /= scond;
  /* L60: */
  	}
      }
  
  /*     Set INFO = N+1 if the matrix is singular to working precision. */
  
      if (*rcond < dlamch_("Epsilon")) {
  	*info = *n + 1;
      }
  
      return 0;
  
  /*     End of ZPPSVX */
  
  } /* zppsvx_ */
  
  