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]/df(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;
  static integer c_n1 = -1;
  static real c_b19 = 1.f;
  
  /* > \brief \b SSYGVX */
  
  /*  =========== DOCUMENTATION =========== */
  
  /* Online html documentation available at */
  /*            http://www.netlib.org/lapack/explore-html/ */
  
  /* > \htmlonly */
  /* > Download SSYGVX + dependencies */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssygvx.
  f"> */
  /* > [TGZ]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssygvx.
  f"> */
  /* > [ZIP]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssygvx.
  f"> */
  /* > [TXT]</a> */
  /* > \endhtmlonly */
  
  /*  Definition: */
  /*  =========== */
  
  /*       SUBROUTINE SSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, */
  /*                          VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, */
  /*                          LWORK, IWORK, IFAIL, INFO ) */
  
  /*       CHARACTER          JOBZ, RANGE, UPLO */
  /*       INTEGER            IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N */
  /*       REAL               ABSTOL, VL, VU */
  /*       INTEGER            IFAIL( * ), IWORK( * ) */
  /*       REAL               A( LDA, * ), B( LDB, * ), W( * ), WORK( * ), */
  /*      $                   Z( LDZ, * ) */
  
  
  /* > \par Purpose: */
  /*  ============= */
  /* > */
  /* > \verbatim */
  /* > */
  /* > SSYGVX computes selected eigenvalues, and optionally, eigenvectors */
  /* > of a real generalized symmetric-definite eigenproblem, of the form */
  /* > A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A */
  /* > and B are assumed to be symmetric and B is also positive definite. */
  /* > Eigenvalues and eigenvectors can be selected by specifying either a */
  /* > range of values or a range of indices for the desired eigenvalues. */
  /* > \endverbatim */
  
  /*  Arguments: */
  /*  ========== */
  
  /* > \param[in] ITYPE */
  /* > \verbatim */
  /* >          ITYPE is INTEGER */
  /* >          Specifies the problem type to be solved: */
  /* >          = 1:  A*x = (lambda)*B*x */
  /* >          = 2:  A*B*x = (lambda)*x */
  /* >          = 3:  B*A*x = (lambda)*x */
  /* > \endverbatim */
  /* > */
  /* > \param[in] JOBZ */
  /* > \verbatim */
  /* >          JOBZ is CHARACTER*1 */
  /* >          = 'N':  Compute eigenvalues only; */
  /* >          = 'V':  Compute eigenvalues and eigenvectors. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] RANGE */
  /* > \verbatim */
  /* >          RANGE is CHARACTER*1 */
  /* >          = 'A': all eigenvalues will be found. */
  /* >          = 'V': all eigenvalues in the half-open interval (VL,VU] */
  /* >                 will be found. */
  /* >          = 'I': the IL-th through IU-th eigenvalues will be found. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] UPLO */
  /* > \verbatim */
  /* >          UPLO is CHARACTER*1 */
  /* >          = 'U':  Upper triangle of A and B are stored; */
  /* >          = 'L':  Lower triangle of A and B are stored. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] N */
  /* > \verbatim */
  /* >          N is INTEGER */
  /* >          The order of the matrix pencil (A,B).  N >= 0. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] A */
  /* > \verbatim */
  /* >          A is REAL array, dimension (LDA, N) */
  /* >          On entry, 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.  If UPLO = 'L', */
  /* >          the leading N-by-N lower triangular part of A contains */
  /* >          the lower triangular part of the matrix A. */
  /* > */
  /* >          On exit, the lower triangle (if UPLO='L') or the upper */
  /* >          triangle (if UPLO='U') of A, including the diagonal, is */
  /* >          destroyed. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LDA */
  /* > \verbatim */
  /* >          LDA is INTEGER */
  /* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] B */
  /* > \verbatim */
  /* >          B is REAL array, dimension (LDB, N) */
  /* >          On entry, the symmetric matrix B.  If UPLO = 'U', the */
  /* >          leading N-by-N upper triangular part of B contains the */
  /* >          upper triangular part of the matrix B.  If UPLO = 'L', */
  /* >          the leading N-by-N lower triangular part of B contains */
  /* >          the lower triangular part of the matrix B. */
  /* > */
  /* >          On exit, if INFO <= N, the part of B containing the matrix is */
  /* >          overwritten by the triangular factor U or L from the Cholesky */
  /* >          factorization B = U**T*U or B = L*L**T. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LDB */
  /* > \verbatim */
  /* >          LDB is INTEGER */
  /* >          The leading dimension of the array B.  LDB >= f2cmax(1,N). */
  /* > \endverbatim */
  /* > */
  /* > \param[in] VL */
  /* > \verbatim */
  /* >          VL is REAL */
  /* >          If RANGE='V', the lower bound of the interval to */
  /* >          be searched for eigenvalues. VL < VU. */
  /* >          Not referenced if RANGE = 'A' or 'I'. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] VU */
  /* > \verbatim */
  /* >          VU is REAL */
  /* >          If RANGE='V', the upper bound of the interval to */
  /* >          be searched for eigenvalues. VL < VU. */
  /* >          Not referenced if RANGE = 'A' or 'I'. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] IL */
  /* > \verbatim */
  /* >          IL is INTEGER */
  /* >          If RANGE='I', the index of the */
  /* >          smallest eigenvalue to be returned. */
  /* >          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
  /* >          Not referenced if RANGE = 'A' or 'V'. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] IU */
  /* > \verbatim */
  /* >          IU is INTEGER */
  /* >          If RANGE='I', the index of the */
  /* >          largest eigenvalue to be returned. */
  /* >          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
  /* >          Not referenced if RANGE = 'A' or 'V'. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] ABSTOL */
  /* > \verbatim */
  /* >          ABSTOL is REAL */
  /* >          The absolute error tolerance for the eigenvalues. */
  /* >          An approximate eigenvalue is accepted as converged */
  /* >          when it is determined to lie in an interval [a,b] */
  /* >          of width less than or equal to */
  /* > */
  /* >                  ABSTOL + EPS *   f2cmax( |a|,|b| ) , */
  /* > */
  /* >          where EPS is the machine precision.  If ABSTOL is less than */
  /* >          or equal to zero, then  EPS*|T|  will be used in its place, */
  /* >          where |T| is the 1-norm of the tridiagonal matrix obtained */
  /* >          by reducing C to tridiagonal form, where C is the symmetric */
  /* >          matrix of the standard symmetric problem to which the */
  /* >          generalized problem is transformed. */
  /* > */
  /* >          Eigenvalues will be computed most accurately when ABSTOL is */
  /* >          set to twice the underflow threshold 2*DLAMCH('S'), not zero. */
  /* >          If this routine returns with INFO>0, indicating that some */
  /* >          eigenvectors did not converge, try setting ABSTOL to */
  /* >          2*SLAMCH('S'). */
  /* > \endverbatim */
  /* > */
  /* > \param[out] M */
  /* > \verbatim */
  /* >          M is INTEGER */
  /* >          The total number of eigenvalues found.  0 <= M <= N. */
  /* >          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] W */
  /* > \verbatim */
  /* >          W is REAL array, dimension (N) */
  /* >          On normal exit, the first M elements contain the selected */
  /* >          eigenvalues in ascending order. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] Z */
  /* > \verbatim */
  /* >          Z is REAL array, dimension (LDZ, f2cmax(1,M)) */
  /* >          If JOBZ = 'N', then Z is not referenced. */
  /* >          If JOBZ = 'V', then if INFO = 0, the first M columns of Z */
  /* >          contain the orthonormal eigenvectors of the matrix A */
  /* >          corresponding to the selected eigenvalues, with the i-th */
  /* >          column of Z holding the eigenvector associated with W(i). */
  /* >          The eigenvectors are normalized as follows: */
  /* >          if ITYPE = 1 or 2, Z**T*B*Z = I; */
  /* >          if ITYPE = 3, Z**T*inv(B)*Z = I. */
  /* > */
  /* >          If an eigenvector fails to converge, then that column of Z */
  /* >          contains the latest approximation to the eigenvector, and the */
  /* >          index of the eigenvector is returned in IFAIL. */
  /* >          Note: the user must ensure that at least f2cmax(1,M) columns are */
  /* >          supplied in the array Z; if RANGE = 'V', the exact value of M */
  /* >          is not known in advance and an upper bound must be used. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LDZ */
  /* > \verbatim */
  /* >          LDZ is INTEGER */
  /* >          The leading dimension of the array Z.  LDZ >= 1, and if */
  /* >          JOBZ = 'V', LDZ >= f2cmax(1,N). */
  /* > \endverbatim */
  /* > */
  /* > \param[out] WORK */
  /* > \verbatim */
  /* >          WORK is REAL 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 the array WORK.  LWORK >= f2cmax(1,8*N). */
  /* >          For optimal efficiency, LWORK >= (NB+3)*N, */
  /* >          where NB is the blocksize for SSYTRD returned by ILAENV. */
  /* > */
  /* >          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 (5*N) */
  /* > \endverbatim */
  /* > */
  /* > \param[out] IFAIL */
  /* > \verbatim */
  /* >          IFAIL is INTEGER array, dimension (N) */
  /* >          If JOBZ = 'V', then if INFO = 0, the first M elements of */
  /* >          IFAIL are zero.  If INFO > 0, then IFAIL contains the */
  /* >          indices of the eigenvectors that failed to converge. */
  /* >          If JOBZ = 'N', then IFAIL is not referenced. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] INFO */
  /* > \verbatim */
  /* >          INFO is INTEGER */
  /* >          = 0:  successful exit */
  /* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
  /* >          > 0:  SPOTRF or SSYEVX returned an error code: */
  /* >             <= N:  if INFO = i, SSYEVX failed to converge; */
  /* >                    i eigenvectors failed to converge.  Their indices */
  /* >                    are stored in array IFAIL. */
  /* >             > N:   if INFO = N + i, for 1 <= i <= N, then the leading */
  /* >                    minor of order i of B is not positive definite. */
  /* >                    The factorization of B could not be completed and */
  /* >                    no eigenvalues or eigenvectors were computed. */
  /* > \endverbatim */
  
  /*  Authors: */
  /*  ======== */
  
  /* > \author Univ. of Tennessee */
  /* > \author Univ. of California Berkeley */
  /* > \author Univ. of Colorado Denver */
  /* > \author NAG Ltd. */
  
  /* > \date June 2016 */
  
  /* > \ingroup realSYeigen */
  
  /* > \par Contributors: */
  /*  ================== */
  /* > */
  /* >     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
  
  /*  ===================================================================== */
  /* Subroutine */ int ssygvx_(integer *itype, char *jobz, char *range, char *
  	uplo, integer *n, real *a, integer *lda, real *b, integer *ldb, real *
  	vl, real *vu, integer *il, integer *iu, real *abstol, integer *m, 
  	real *w, real *z__, integer *ldz, real *work, integer *lwork, integer 
  	*iwork, integer *ifail, integer *info)
  {
      /* System generated locals */
      integer a_dim1, a_offset, b_dim1, b_offset, z_dim1, z_offset, i__1, i__2;
  
      /* Local variables */
      extern logical lsame_(char *, char *);
      char trans[1];
      logical upper;
      extern /* Subroutine */ int strmm_(char *, char *, char *, char *, 
  	    integer *, integer *, real *, real *, integer *, real *, integer *
  	    );
      logical wantz;
      extern /* Subroutine */ int strsm_(char *, char *, char *, char *, 
  	    integer *, integer *, real *, real *, integer *, real *, integer *
  	    );
      integer nb;
      logical alleig, indeig, valeig;
      extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
      extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
  	    integer *, integer *, ftnlen, ftnlen);
      integer lwkmin;
      extern /* Subroutine */ int spotrf_(char *, integer *, real *, integer *, 
  	    integer *);
      integer lwkopt;
      logical lquery;
      extern /* Subroutine */ int ssygst_(integer *, char *, integer *, real *, 
  	    integer *, real *, integer *, integer *), ssyevx_(char *, 
  	    char *, char *, integer *, real *, integer *, real *, real *, 
  	    integer *, integer *, real *, integer *, real *, real *, integer *
  	    , real *, integer *, integer *, integer *, integer *);
  
  
  /*  -- LAPACK driver routine (version 3.7.1) -- */
  /*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
  /*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  /*     June 2016 */
  
  
  /* ===================================================================== */
  
  
  /*     Test the input parameters. */
  
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1 * 1;
      a -= a_offset;
      b_dim1 = *ldb;
      b_offset = 1 + b_dim1 * 1;
      b -= b_offset;
      --w;
      z_dim1 = *ldz;
      z_offset = 1 + z_dim1 * 1;
      z__ -= z_offset;
      --work;
      --iwork;
      --ifail;
  
      /* Function Body */
      upper = lsame_(uplo, "U");
      wantz = lsame_(jobz, "V");
      alleig = lsame_(range, "A");
      valeig = lsame_(range, "V");
      indeig = lsame_(range, "I");
      lquery = *lwork == -1;
  
      *info = 0;
      if (*itype < 1 || *itype > 3) {
  	*info = -1;
      } else if (! (wantz || lsame_(jobz, "N"))) {
  	*info = -2;
      } else if (! (alleig || valeig || indeig)) {
  	*info = -3;
      } else if (! (upper || lsame_(uplo, "L"))) {
  	*info = -4;
      } else if (*n < 0) {
  	*info = -5;
      } else if (*lda < f2cmax(1,*n)) {
  	*info = -7;
      } else if (*ldb < f2cmax(1,*n)) {
  	*info = -9;
      } else {
  	if (valeig) {
  	    if (*n > 0 && *vu <= *vl) {
  		*info = -11;
  	    }
  	} else if (indeig) {
  	    if (*il < 1 || *il > f2cmax(1,*n)) {
  		*info = -12;
  	    } else if (*iu < f2cmin(*n,*il) || *iu > *n) {
  		*info = -13;
  	    }
  	}
      }
      if (*info == 0) {
  	if (*ldz < 1 || wantz && *ldz < *n) {
  	    *info = -18;
  	}
      }
  
      if (*info == 0) {
  /* Computing MAX */
  	i__1 = 1, i__2 = *n << 3;
  	lwkmin = f2cmax(i__1,i__2);
  	nb = ilaenv_(&c__1, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
  		 (ftnlen)1);
  /* Computing MAX */
  	i__1 = lwkmin, i__2 = (nb + 3) * *n;
  	lwkopt = f2cmax(i__1,i__2);
  	work[1] = (real) lwkopt;
  
  	if (*lwork < lwkmin && ! lquery) {
  	    *info = -20;
  	}
      }
  
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("SSYGVX", &i__1, (ftnlen)6);
  	return 0;
      } else if (lquery) {
  	return 0;
      }
  
  /*     Quick return if possible */
  
      *m = 0;
      if (*n == 0) {
  	return 0;
      }
  
  /*     Form a Cholesky factorization of B. */
  
      spotrf_(uplo, n, &b[b_offset], ldb, info);
      if (*info != 0) {
  	*info = *n + *info;
  	return 0;
      }
  
  /*     Transform problem to standard eigenvalue problem and solve. */
  
      ssygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
      ssyevx_(jobz, range, uplo, n, &a[a_offset], lda, vl, vu, il, iu, abstol, 
  	    m, &w[1], &z__[z_offset], ldz, &work[1], lwork, &iwork[1], &ifail[
  	    1], info);
  
      if (wantz) {
  
  /*        Backtransform eigenvectors to the original problem. */
  
  	if (*info > 0) {
  	    *m = *info - 1;
  	}
  	if (*itype == 1 || *itype == 2) {
  
  /*           For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */
  /*           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y */
  
  	    if (upper) {
  		*(unsigned char *)trans = 'N';
  	    } else {
  		*(unsigned char *)trans = 'T';
  	    }
  
  	    strsm_("Left", uplo, trans, "Non-unit", n, m, &c_b19, &b[b_offset]
  		    , ldb, &z__[z_offset], ldz);
  
  	} else if (*itype == 3) {
  
  /*           For B*A*x=(lambda)*x; */
  /*           backtransform eigenvectors: x = L*y or U**T*y */
  
  	    if (upper) {
  		*(unsigned char *)trans = 'T';
  	    } else {
  		*(unsigned char *)trans = 'N';
  	    }
  
  	    strmm_("Left", uplo, trans, "Non-unit", n, m, &c_b19, &b[b_offset]
  		    , ldb, &z__[z_offset], ldz);
  	}
      }
  
  /*     Set WORK(1) to optimal workspace size. */
  
      work[1] = (real) lwkopt;
  
      return 0;
  
  /*     End of SSYGVX */
  
  } /* ssygvx_ */
  
  