OpenBLAS/lapack-netlib/SRC/dlarrv.c

#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 doublereal c_b5 = 0.;
static integer c__1 = 1;
static integer c__2 = 2;

/* > \brief \b DLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenv
alues of L D LT. */

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

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

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

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

/*       SUBROUTINE DLARRV( N, VL, VU, D, L, PIVMIN, */
/*                          ISPLIT, M, DOL, DOU, MINRGP, */
/*                          RTOL1, RTOL2, W, WERR, WGAP, */
/*                          IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, */
/*                          WORK, IWORK, INFO ) */

/*       INTEGER            DOL, DOU, INFO, LDZ, M, N */
/*       DOUBLE PRECISION   MINRGP, PIVMIN, RTOL1, RTOL2, VL, VU */
/*       INTEGER            IBLOCK( * ), INDEXW( * ), ISPLIT( * ), */
/*      $                   ISUPPZ( * ), IWORK( * ) */
/*       DOUBLE PRECISION   D( * ), GERS( * ), L( * ), W( * ), WERR( * ), */
/*      $                   WGAP( * ), WORK( * ) */
/*       DOUBLE PRECISION  Z( LDZ, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLARRV computes the eigenvectors of the tridiagonal matrix */
/* > T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T. */
/* > The input eigenvalues should have been computed by DLARRE. */
/* > \endverbatim */

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

/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] VL */
/* > \verbatim */
/* >          VL is DOUBLE PRECISION */
/* >          Lower bound of the interval that contains the desired */
/* >          eigenvalues. VL < VU. Needed to compute gaps on the left or right */
/* >          end of the extremal eigenvalues in the desired RANGE. */
/* > \endverbatim */
/* > */
/* > \param[in] VU */
/* > \verbatim */
/* >          VU is DOUBLE PRECISION */
/* >          Upper bound of the interval that contains the desired */
/* >          eigenvalues. VL < VU. */
/* >          Note: VU is currently not used by this implementation of DLARRV, VU is */
/* >          passed to DLARRV because it could be used compute gaps on the right end */
/* >          of the extremal eigenvalues. However, with not much initial accuracy in */
/* >          LAMBDA and VU, the formula can lead to an overestimation of the right gap */
/* >          and thus to inadequately early RQI 'convergence'. This is currently */
/* >          prevented this by forcing a small right gap. And so it turns out that VU */
/* >          is currently not used by this implementation of DLARRV. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* >          D is DOUBLE PRECISION array, dimension (N) */
/* >          On entry, the N diagonal elements of the diagonal matrix D. */
/* >          On exit, D may be overwritten. */
/* > \endverbatim */
/* > */
/* > \param[in,out] L */
/* > \verbatim */
/* >          L is DOUBLE PRECISION array, dimension (N) */
/* >          On entry, the (N-1) subdiagonal elements of the unit */
/* >          bidiagonal matrix L are in elements 1 to N-1 of L */
/* >          (if the matrix is not split.) At the end of each block */
/* >          is stored the corresponding shift as given by DLARRE. */
/* >          On exit, L is overwritten. */
/* > \endverbatim */
/* > */
/* > \param[in] PIVMIN */
/* > \verbatim */
/* >          PIVMIN is DOUBLE PRECISION */
/* >          The minimum pivot allowed in the Sturm sequence. */
/* > \endverbatim */
/* > */
/* > \param[in] ISPLIT */
/* > \verbatim */
/* >          ISPLIT is INTEGER array, dimension (N) */
/* >          The splitting points, at which T breaks up into blocks. */
/* >          The first block consists of rows/columns 1 to */
/* >          ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 */
/* >          through ISPLIT( 2 ), etc. */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The total number of input eigenvalues.  0 <= M <= N. */
/* > \endverbatim */
/* > */
/* > \param[in] DOL */
/* > \verbatim */
/* >          DOL is INTEGER */
/* > \endverbatim */
/* > */
/* > \param[in] DOU */
/* > \verbatim */
/* >          DOU is INTEGER */
/* >          If the user wants to compute only selected eigenvectors from all */
/* >          the eigenvalues supplied, he can specify an index range DOL:DOU. */
/* >          Or else the setting DOL=1, DOU=M should be applied. */
/* >          Note that DOL and DOU refer to the order in which the eigenvalues */
/* >          are stored in W. */
/* >          If the user wants to compute only selected eigenpairs, then */
/* >          the columns DOL-1 to DOU+1 of the eigenvector space Z contain the */
/* >          computed eigenvectors. All other columns of Z are set to zero. */
/* > \endverbatim */
/* > */
/* > \param[in] MINRGP */
/* > \verbatim */
/* >          MINRGP is DOUBLE PRECISION */
/* > \endverbatim */
/* > */
/* > \param[in] RTOL1 */
/* > \verbatim */
/* >          RTOL1 is DOUBLE PRECISION */
/* > \endverbatim */
/* > */
/* > \param[in] RTOL2 */
/* > \verbatim */
/* >          RTOL2 is DOUBLE PRECISION */
/* >           Parameters for bisection. */
/* >           An interval [LEFT,RIGHT] has converged if */
/* >           RIGHT-LEFT < MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) */
/* > \endverbatim */
/* > */
/* > \param[in,out] W */
/* > \verbatim */
/* >          W is DOUBLE PRECISION array, dimension (N) */
/* >          The first M elements of W contain the APPROXIMATE eigenvalues for */
/* >          which eigenvectors are to be computed.  The eigenvalues */
/* >          should be grouped by split-off block and ordered from */
/* >          smallest to largest within the block ( The output array */
/* >          W from DLARRE is expected here ). Furthermore, they are with */
/* >          respect to the shift of the corresponding root representation */
/* >          for their block. On exit, W holds the eigenvalues of the */
/* >          UNshifted matrix. */
/* > \endverbatim */
/* > */
/* > \param[in,out] WERR */
/* > \verbatim */
/* >          WERR is DOUBLE PRECISION array, dimension (N) */
/* >          The first M elements contain the semiwidth of the uncertainty */
/* >          interval of the corresponding eigenvalue in W */
/* > \endverbatim */
/* > */
/* > \param[in,out] WGAP */
/* > \verbatim */
/* >          WGAP is DOUBLE PRECISION array, dimension (N) */
/* >          The separation from the right neighbor eigenvalue in W. */
/* > \endverbatim */
/* > */
/* > \param[in] IBLOCK */
/* > \verbatim */
/* >          IBLOCK is INTEGER array, dimension (N) */
/* >          The indices of the blocks (submatrices) associated with the */
/* >          corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue */
/* >          W(i) belongs to the first block from the top, =2 if W(i) */
/* >          belongs to the second block, etc. */
/* > \endverbatim */
/* > */
/* > \param[in] INDEXW */
/* > \verbatim */
/* >          INDEXW is INTEGER array, dimension (N) */
/* >          The indices of the eigenvalues within each block (submatrix); */
/* >          for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the */
/* >          i-th eigenvalue W(i) is the 10-th eigenvalue in the second block. */
/* > \endverbatim */
/* > */
/* > \param[in] GERS */
/* > \verbatim */
/* >          GERS is DOUBLE PRECISION array, dimension (2*N) */
/* >          The N Gerschgorin intervals (the i-th Gerschgorin interval */
/* >          is (GERS(2*i-1), GERS(2*i)). The Gerschgorin intervals should */
/* >          be computed from the original UNshifted matrix. */
/* > \endverbatim */
/* > */
/* > \param[out] Z */
/* > \verbatim */
/* >          Z is DOUBLE PRECISION array, dimension (LDZ, f2cmax(1,M) ) */
/* >          If INFO = 0, the first M columns of Z contain the */
/* >          orthonormal eigenvectors of the matrix T */
/* >          corresponding to the input eigenvalues, with the i-th */
/* >          column of Z holding the eigenvector associated with W(i). */
/* >          Note: the user must ensure that at least f2cmax(1,M) columns are */
/* >          supplied in the array Z. */
/* > \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] ISUPPZ */
/* > \verbatim */
/* >          ISUPPZ is INTEGER array, dimension ( 2*f2cmax(1,M) ) */
/* >          The support of the eigenvectors in Z, i.e., the indices */
/* >          indicating the nonzero elements in Z. The I-th eigenvector */
/* >          is nonzero only in elements ISUPPZ( 2*I-1 ) through */
/* >          ISUPPZ( 2*I ). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is DOUBLE PRECISION array, dimension (12*N) */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (7*N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit */
/* > */
/* >          > 0:  A problem occurred in DLARRV. */
/* >          < 0:  One of the called subroutines signaled an internal problem. */
/* >                Needs inspection of the corresponding parameter IINFO */
/* >                for further information. */
/* > */
/* >          =-1:  Problem in DLARRB when refining a child's eigenvalues. */
/* >          =-2:  Problem in DLARRF when computing the RRR of a child. */
/* >                When a child is inside a tight cluster, it can be difficult */
/* >                to find an RRR. A partial remedy from the user's point of */
/* >                view is to make the parameter MINRGP smaller and recompile. */
/* >                However, as the orthogonality of the computed vectors is */
/* >                proportional to 1/MINRGP, the user should be aware that */
/* >                he might be trading in precision when he decreases MINRGP. */
/* >          =-3:  Problem in DLARRB when refining a single eigenvalue */
/* >                after the Rayleigh correction was rejected. */
/* >          = 5:  The Rayleigh Quotient Iteration failed to converge to */
/* >                full accuracy in MAXITR steps. */
/* > \endverbatim */

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

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

/* > \date June 2016 */

/* > \ingroup doubleOTHERauxiliary */

/* > \par Contributors: */
/*  ================== */
/* > */
/* > Beresford Parlett, University of California, Berkeley, USA \n */
/* > Jim Demmel, University of California, Berkeley, USA \n */
/* > Inderjit Dhillon, University of Texas, Austin, USA \n */
/* > Osni Marques, LBNL/NERSC, USA \n */
/* > Christof Voemel, University of California, Berkeley, USA */

/*  ===================================================================== */
/* Subroutine */ void dlarrv_(integer *n, doublereal *vl, doublereal *vu, 
	doublereal *d__, doublereal *l, doublereal *pivmin, integer *isplit, 
	integer *m, integer *dol, integer *dou, doublereal *minrgp, 
	doublereal *rtol1, doublereal *rtol2, doublereal *w, doublereal *werr,
	 doublereal *wgap, integer *iblock, integer *indexw, doublereal *gers,
	 doublereal *z__, integer *ldz, integer *isuppz, doublereal *work, 
	integer *iwork, integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5;
    doublereal d__1, d__2;
    logical L__1;

    /* Local variables */
    integer iend, jblk;
    doublereal lgap;
    integer done;
    doublereal rgap, left;
    integer wend, iter;
    doublereal bstw;
    integer minwsize, itmp1, i__, j, k, p, q;
    extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    integer indld;
    doublereal fudge;
    integer idone;
    doublereal sigma;
    integer iinfo, iindr;
    doublereal resid;
    logical eskip;
    doublereal right;
    extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    integer nclus, zfrom;
    doublereal rqtol;
    integer iindc1, iindc2;
    extern /* Subroutine */ void dlar1v_(integer *, integer *, integer *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, logical *,
	     integer *, doublereal *, doublereal *, integer *, integer *, 
	    doublereal *, doublereal *, doublereal *, doublereal *);
    integer miniwsize;
    logical stp2ii;
    doublereal lambda;
    integer ii;
    doublereal gl;
    integer im, in;
    extern doublereal dlamch_(char *);
    doublereal gu;
    integer ibegin, indeig;
    logical needbs;
    integer indlld;
    doublereal sgndef, mingma;
    extern /* Subroutine */ void dlarrb_(integer *, doublereal *, doublereal *,
	     integer *, integer *, doublereal *, doublereal *, integer *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, integer *,
	     doublereal *, doublereal *, integer *, integer *);
    integer oldien, oldncl, wbegin, negcnt;
    doublereal spdiam;
    integer oldcls;
    doublereal savgap;
    integer ndepth;
    doublereal ssigma;
    extern /* Subroutine */ void dlarrf_(integer *, doublereal *, doublereal *,
	     doublereal *, integer *, integer *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, 
	    doublereal *, integer *);
    logical usedbs;
    integer iindwk, offset;
    doublereal gaptol;
    extern /* Subroutine */ void dlaset_(char *, integer *, integer *, 
	    doublereal *, doublereal *, doublereal *, integer *);
    integer newcls, oldfst, indwrk, windex, oldlst;
    logical usedrq;
    integer newfst, newftt, parity, windmn, windpl, isupmn, newlst, zusedl;
    doublereal bstres;
    integer newsiz, zusedu, zusedw;
    doublereal nrminv, rqcorr;
    logical tryrqc;
    integer isupmx;
    doublereal gap, eps, tau, tol, tmp;
    integer zto;
    doublereal ztz;


/*  -- LAPACK auxiliary routine (version 3.8.0) -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/*     June 2016 */


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

    /* Parameter adjustments */
    --d__;
    --l;
    --isplit;
    --w;
    --werr;
    --wgap;
    --iblock;
    --indexw;
    --gers;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --isuppz;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;

/*     Quick return if possible */

    if (*n <= 0 || *m <= 0) {
	return;
    }

/*     The first N entries of WORK are reserved for the eigenvalues */
    indld = *n + 1;
    indlld = (*n << 1) + 1;
    indwrk = *n * 3 + 1;
    minwsize = *n * 12;
    i__1 = minwsize;
    for (i__ = 1; i__ <= i__1; ++i__) {
	work[i__] = 0.;
/* L5: */
    }
/*     IWORK(IINDR+1:IINDR+N) hold the twist indices R for the */
/*     factorization used to compute the FP vector */
    iindr = 0;
/*     IWORK(IINDC1+1:IINC2+N) are used to store the clusters of the current */
/*     layer and the one above. */
    iindc1 = *n;
    iindc2 = *n << 1;
    iindwk = *n * 3 + 1;
    miniwsize = *n * 7;
    i__1 = miniwsize;
    for (i__ = 1; i__ <= i__1; ++i__) {
	iwork[i__] = 0;
/* L10: */
    }
    zusedl = 1;
    if (*dol > 1) {
/*        Set lower bound for use of Z */
	zusedl = *dol - 1;
    }
    zusedu = *m;
    if (*dou < *m) {
/*        Set lower bound for use of Z */
	zusedu = *dou + 1;
    }
/*     The width of the part of Z that is used */
    zusedw = zusedu - zusedl + 1;
    dlaset_("Full", n, &zusedw, &c_b5, &c_b5, &z__[zusedl * z_dim1 + 1], ldz);
    eps = dlamch_("Precision");
    rqtol = eps * 2.;

/*     Set expert flags for standard code. */
    tryrqc = TRUE_;
    if (*dol == 1 && *dou == *m) {
    } else {
/*        Only selected eigenpairs are computed. Since the other evalues */
/*        are not refined by RQ iteration, bisection has to compute to full */
/*        accuracy. */
	*rtol1 = eps * 4.;
	*rtol2 = eps * 4.;
    }
/*     The entries WBEGIN:WEND in W, WERR, WGAP correspond to the */
/*     desired eigenvalues. The support of the nonzero eigenvector */
/*     entries is contained in the interval IBEGIN:IEND. */
/*     Remark that if k eigenpairs are desired, then the eigenvectors */
/*     are stored in k contiguous columns of Z. */
/*     DONE is the number of eigenvectors already computed */
    done = 0;
    ibegin = 1;
    wbegin = 1;
    i__1 = iblock[*m];
    for (jblk = 1; jblk <= i__1; ++jblk) {
	iend = isplit[jblk];
	sigma = l[iend];
/*        Find the eigenvectors of the submatrix indexed IBEGIN */
/*        through IEND. */
	wend = wbegin - 1;
L15:
	if (wend < *m) {
	    if (iblock[wend + 1] == jblk) {
		++wend;
		goto L15;
	    }
	}
	if (wend < wbegin) {
	    ibegin = iend + 1;
	    goto L170;
	} else if (wend < *dol || wbegin > *dou) {
	    ibegin = iend + 1;
	    wbegin = wend + 1;
	    goto L170;
	}
/*        Find local spectral diameter of the block */
	gl = gers[(ibegin << 1) - 1];
	gu = gers[ibegin * 2];
	i__2 = iend;
	for (i__ = ibegin + 1; i__ <= i__2; ++i__) {
/* Computing MIN */
	    d__1 = gers[(i__ << 1) - 1];
	    gl = f2cmin(d__1,gl);
/* Computing MAX */
	    d__1 = gers[i__ * 2];
	    gu = f2cmax(d__1,gu);
/* L20: */
	}
	spdiam = gu - gl;
/*        OLDIEN is the last index of the previous block */
	oldien = ibegin - 1;
/*        Calculate the size of the current block */
	in = iend - ibegin + 1;
/*        The number of eigenvalues in the current block */
	im = wend - wbegin + 1;
/*        This is for a 1x1 block */
	if (ibegin == iend) {
	    ++done;
	    z__[ibegin + wbegin * z_dim1] = 1.;
	    isuppz[(wbegin << 1) - 1] = ibegin;
	    isuppz[wbegin * 2] = ibegin;
	    w[wbegin] += sigma;
	    work[wbegin] = w[wbegin];
	    ibegin = iend + 1;
	    ++wbegin;
	    goto L170;
	}
/*        The desired (shifted) eigenvalues are stored in W(WBEGIN:WEND) */
/*        Note that these can be approximations, in this case, the corresp. */
/*        entries of WERR give the size of the uncertainty interval. */
/*        The eigenvalue approximations will be refined when necessary as */
/*        high relative accuracy is required for the computation of the */
/*        corresponding eigenvectors. */
	dcopy_(&im, &w[wbegin], &c__1, &work[wbegin], &c__1);
/*        We store in W the eigenvalue approximations w.r.t. the original */
/*        matrix T. */
	i__2 = im;
	for (i__ = 1; i__ <= i__2; ++i__) {
	    w[wbegin + i__ - 1] += sigma;
/* L30: */
	}
/*        NDEPTH is the current depth of the representation tree */
	ndepth = 0;
/*        PARITY is either 1 or 0 */
	parity = 1;
/*        NCLUS is the number of clusters for the next level of the */
/*        representation tree, we start with NCLUS = 1 for the root */
	nclus = 1;
	iwork[iindc1 + 1] = 1;
	iwork[iindc1 + 2] = im;
/*        IDONE is the number of eigenvectors already computed in the current */
/*        block */
	idone = 0;
/*        loop while( IDONE.LT.IM ) */
/*        generate the representation tree for the current block and */
/*        compute the eigenvectors */
L40:
	if (idone < im) {
/*           This is a crude protection against infinitely deep trees */
	    if (ndepth > *m) {
		*info = -2;
		return;
	    }
/*           breadth first processing of the current level of the representation */
/*           tree: OLDNCL = number of clusters on current level */
	    oldncl = nclus;
/*           reset NCLUS to count the number of child clusters */
	    nclus = 0;

	    parity = 1 - parity;
	    if (parity == 0) {
		oldcls = iindc1;
		newcls = iindc2;
	    } else {
		oldcls = iindc2;
		newcls = iindc1;
	    }
/*           Process the clusters on the current level */
	    i__2 = oldncl;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		j = oldcls + (i__ << 1);
/*              OLDFST, OLDLST = first, last index of current cluster. */
/*                               cluster indices start with 1 and are relative */
/*                               to WBEGIN when accessing W, WGAP, WERR, Z */
		oldfst = iwork[j - 1];
		oldlst = iwork[j];
		if (ndepth > 0) {
/*                 Retrieve relatively robust representation (RRR) of cluster */
/*                 that has been computed at the previous level */
/*                 The RRR is stored in Z and overwritten once the eigenvectors */
/*                 have been computed or when the cluster is refined */
		    if (*dol == 1 && *dou == *m) {
/*                    Get representation from location of the leftmost evalue */
/*                    of the cluster */
			j = wbegin + oldfst - 1;
		    } else {
			if (wbegin + oldfst - 1 < *dol) {
/*                       Get representation from the left end of Z array */
			    j = *dol - 1;
			} else if (wbegin + oldfst - 1 > *dou) {
/*                       Get representation from the right end of Z array */
			    j = *dou;
			} else {
			    j = wbegin + oldfst - 1;
			}
		    }
		    dcopy_(&in, &z__[ibegin + j * z_dim1], &c__1, &d__[ibegin]
			    , &c__1);
		    i__3 = in - 1;
		    dcopy_(&i__3, &z__[ibegin + (j + 1) * z_dim1], &c__1, &l[
			    ibegin], &c__1);
		    sigma = z__[iend + (j + 1) * z_dim1];
/*                 Set the corresponding entries in Z to zero */
		    dlaset_("Full", &in, &c__2, &c_b5, &c_b5, &z__[ibegin + j 
			    * z_dim1], ldz);
		}
/*              Compute DL and DLL of current RRR */
		i__3 = iend - 1;
		for (j = ibegin; j <= i__3; ++j) {
		    tmp = d__[j] * l[j];
		    work[indld - 1 + j] = tmp;
		    work[indlld - 1 + j] = tmp * l[j];
/* L50: */
		}
		if (ndepth > 0) {
/*                 P and Q are index of the first and last eigenvalue to compute */
/*                 within the current block */
		    p = indexw[wbegin - 1 + oldfst];
		    q = indexw[wbegin - 1 + oldlst];
/*                 Offset for the arrays WORK, WGAP and WERR, i.e., the P-OFFSET */
/*                 through the Q-OFFSET elements of these arrays are to be used. */
/*                  OFFSET = P-OLDFST */
		    offset = indexw[wbegin] - 1;
/*                 perform limited bisection (if necessary) to get approximate */
/*                 eigenvalues to the precision needed. */
		    dlarrb_(&in, &d__[ibegin], &work[indlld + ibegin - 1], &p,
			     &q, rtol1, rtol2, &offset, &work[wbegin], &wgap[
			    wbegin], &werr[wbegin], &work[indwrk], &iwork[
			    iindwk], pivmin, &spdiam, &in, &iinfo);
		    if (iinfo != 0) {
			*info = -1;
			return;
		    }
/*                 We also recompute the extremal gaps. W holds all eigenvalues */
/*                 of the unshifted matrix and must be used for computation */
/*                 of WGAP, the entries of WORK might stem from RRRs with */
/*                 different shifts. The gaps from WBEGIN-1+OLDFST to */
/*                 WBEGIN-1+OLDLST are correctly computed in DLARRB. */
/*                 However, we only allow the gaps to become greater since */
/*                 this is what should happen when we decrease WERR */
		    if (oldfst > 1) {
/* Computing MAX */
			d__1 = wgap[wbegin + oldfst - 2], d__2 = w[wbegin + 
				oldfst - 1] - werr[wbegin + oldfst - 1] - w[
				wbegin + oldfst - 2] - werr[wbegin + oldfst - 
				2];
			wgap[wbegin + oldfst - 2] = f2cmax(d__1,d__2);
		    }
		    if (wbegin + oldlst - 1 < wend) {
/* Computing MAX */
			d__1 = wgap[wbegin + oldlst - 1], d__2 = w[wbegin + 
				oldlst] - werr[wbegin + oldlst] - w[wbegin + 
				oldlst - 1] - werr[wbegin + oldlst - 1];
			wgap[wbegin + oldlst - 1] = f2cmax(d__1,d__2);
		    }
/*                 Each time the eigenvalues in WORK get refined, we store */
/*                 the newly found approximation with all shifts applied in W */
		    i__3 = oldlst;
		    for (j = oldfst; j <= i__3; ++j) {
			w[wbegin + j - 1] = work[wbegin + j - 1] + sigma;
/* L53: */
		    }
		}
/*              Process the current node. */
		newfst = oldfst;
		i__3 = oldlst;
		for (j = oldfst; j <= i__3; ++j) {
		    if (j == oldlst) {
/*                    we are at the right end of the cluster, this is also the */
/*                    boundary of the child cluster */
			newlst = j;
		    } else if (wgap[wbegin + j - 1] >= *minrgp * (d__1 = work[
			    wbegin + j - 1], abs(d__1))) {
/*                    the right relative gap is big enough, the child cluster */
/*                    (NEWFST,..,NEWLST) is well separated from the following */
			newlst = j;
		    } else {
/*                    inside a child cluster, the relative gap is not */
/*                    big enough. */
			goto L140;
		    }
/*                 Compute size of child cluster found */
		    newsiz = newlst - newfst + 1;
/*                 NEWFTT is the place in Z where the new RRR or the computed */
/*                 eigenvector is to be stored */
		    if (*dol == 1 && *dou == *m) {
/*                    Store representation at location of the leftmost evalue */
/*                    of the cluster */
			newftt = wbegin + newfst - 1;
		    } else {
			if (wbegin + newfst - 1 < *dol) {
/*                       Store representation at the left end of Z array */
			    newftt = *dol - 1;
			} else if (wbegin + newfst - 1 > *dou) {
/*                       Store representation at the right end of Z array */
			    newftt = *dou;
			} else {
			    newftt = wbegin + newfst - 1;
			}
		    }
		    if (newsiz > 1) {

/*                    Current child is not a singleton but a cluster. */
/*                    Compute and store new representation of child. */


/*                    Compute left and right cluster gap. */

/*                    LGAP and RGAP are not computed from WORK because */
/*                    the eigenvalue approximations may stem from RRRs */
/*                    different shifts. However, W hold all eigenvalues */
/*                    of the unshifted matrix. Still, the entries in WGAP */
/*                    have to be computed from WORK since the entries */
/*                    in W might be of the same order so that gaps are not */
/*                    exhibited correctly for very close eigenvalues. */
			if (newfst == 1) {
/* Computing MAX */
			    d__1 = 0., d__2 = w[wbegin] - werr[wbegin] - *vl;
			    lgap = f2cmax(d__1,d__2);
			} else {
			    lgap = wgap[wbegin + newfst - 2];
			}
			rgap = wgap[wbegin + newlst - 1];

/*                    Compute left- and rightmost eigenvalue of child */
/*                    to high precision in order to shift as close */
/*                    as possible and obtain as large relative gaps */
/*                    as possible */

			for (k = 1; k <= 2; ++k) {
			    if (k == 1) {
				p = indexw[wbegin - 1 + newfst];
			    } else {
				p = indexw[wbegin - 1 + newlst];
			    }
			    offset = indexw[wbegin] - 1;
			    dlarrb_(&in, &d__[ibegin], &work[indlld + ibegin 
				    - 1], &p, &p, &rqtol, &rqtol, &offset, &
				    work[wbegin], &wgap[wbegin], &werr[wbegin]
				    , &work[indwrk], &iwork[iindwk], pivmin, &
				    spdiam, &in, &iinfo);
/* L55: */
			}

			if (wbegin + newlst - 1 < *dol || wbegin + newfst - 1 
				> *dou) {
/*                       if the cluster contains no desired eigenvalues */
/*                       skip the computation of that branch of the rep. tree */

/*                       We could skip before the refinement of the extremal */
/*                       eigenvalues of the child, but then the representation */
/*                       tree could be different from the one when nothing is */
/*                       skipped. For this reason we skip at this place. */
			    idone = idone + newlst - newfst + 1;
			    goto L139;
			}

/*                    Compute RRR of child cluster. */
/*                    Note that the new RRR is stored in Z */

/*                    DLARRF needs LWORK = 2*N */
			dlarrf_(&in, &d__[ibegin], &l[ibegin], &work[indld + 
				ibegin - 1], &newfst, &newlst, &work[wbegin], 
				&wgap[wbegin], &werr[wbegin], &spdiam, &lgap, 
				&rgap, pivmin, &tau, &z__[ibegin + newftt * 
				z_dim1], &z__[ibegin + (newftt + 1) * z_dim1],
				 &work[indwrk], &iinfo);
			if (iinfo == 0) {
/*                       a new RRR for the cluster was found by DLARRF */
/*                       update shift and store it */
			    ssigma = sigma + tau;
			    z__[iend + (newftt + 1) * z_dim1] = ssigma;
/*                       WORK() are the midpoints and WERR() the semi-width */
/*                       Note that the entries in W are unchanged. */
			    i__4 = newlst;
			    for (k = newfst; k <= i__4; ++k) {
				fudge = eps * 3. * (d__1 = work[wbegin + k - 
					1], abs(d__1));
				work[wbegin + k - 1] -= tau;
				fudge += eps * 4. * (d__1 = work[wbegin + k - 
					1], abs(d__1));
/*                          Fudge errors */
				werr[wbegin + k - 1] += fudge;
/*                          Gaps are not fudged. Provided that WERR is small */
/*                          when eigenvalues are close, a zero gap indicates */
/*                          that a new representation is needed for resolving */
/*                          the cluster. A fudge could lead to a wrong decision */
/*                          of judging eigenvalues 'separated' which in */
/*                          reality are not. This could have a negative impact */
/*                          on the orthogonality of the computed eigenvectors. */
/* L116: */
			    }
			    ++nclus;
			    k = newcls + (nclus << 1);
			    iwork[k - 1] = newfst;
			    iwork[k] = newlst;
			} else {
			    *info = -2;
			    return;
			}
		    } else {

/*                    Compute eigenvector of singleton */

			iter = 0;

			tol = log((doublereal) in) * 4. * eps;

			k = newfst;
			windex = wbegin + k - 1;
/* Computing MAX */
			i__4 = windex - 1;
			windmn = f2cmax(i__4,1);
/* Computing MIN */
			i__4 = windex + 1;
			windpl = f2cmin(i__4,*m);
			lambda = work[windex];
			++done;
/*                    Check if eigenvector computation is to be skipped */
			if (windex < *dol || windex > *dou) {
			    eskip = TRUE_;
			    goto L125;
			} else {
			    eskip = FALSE_;
			}
			left = work[windex] - werr[windex];
			right = work[windex] + werr[windex];
			indeig = indexw[windex];
/*                    Note that since we compute the eigenpairs for a child, */
/*                    all eigenvalue approximations are w.r.t the same shift. */
/*                    In this case, the entries in WORK should be used for */
/*                    computing the gaps since they exhibit even very small */
/*                    differences in the eigenvalues, as opposed to the */
/*                    entries in W which might "look" the same. */
			if (k == 1) {
/*                       In the case RANGE='I' and with not much initial */
/*                       accuracy in LAMBDA and VL, the formula */
/*                       LGAP = MAX( ZERO, (SIGMA - VL) + LAMBDA ) */
/*                       can lead to an overestimation of the left gap and */
/*                       thus to inadequately early RQI 'convergence'. */
/*                       Prevent this by forcing a small left gap. */
/* Computing MAX */
			    d__1 = abs(left), d__2 = abs(right);
			    lgap = eps * f2cmax(d__1,d__2);
			} else {
			    lgap = wgap[windmn];
			}
			if (k == im) {
/*                       In the case RANGE='I' and with not much initial */
/*                       accuracy in LAMBDA and VU, the formula */
/*                       can lead to an overestimation of the right gap and */
/*                       thus to inadequately early RQI 'convergence'. */
/*                       Prevent this by forcing a small right gap. */
/* Computing MAX */
			    d__1 = abs(left), d__2 = abs(right);
			    rgap = eps * f2cmax(d__1,d__2);
			} else {
			    rgap = wgap[windex];
			}
			gap = f2cmin(lgap,rgap);
			if (k == 1 || k == im) {
/*                       The eigenvector support can become wrong */
/*                       because significant entries could be cut off due to a */
/*                       large GAPTOL parameter in LAR1V. Prevent this. */
			    gaptol = 0.;
			} else {
			    gaptol = gap * eps;
			}
			isupmn = in;
			isupmx = 1;
/*                    Update WGAP so that it holds the minimum gap */
/*                    to the left or the right. This is crucial in the */
/*                    case where bisection is used to ensure that the */
/*                    eigenvalue is refined up to the required precision. */
/*                    The correct value is restored afterwards. */
			savgap = wgap[windex];
			wgap[windex] = gap;
/*                    We want to use the Rayleigh Quotient Correction */
/*                    as often as possible since it converges quadratically */
/*                    when we are close enough to the desired eigenvalue. */
/*                    However, the Rayleigh Quotient can have the wrong sign */
/*                    and lead us away from the desired eigenvalue. In this */
/*                    case, the best we can do is to use bisection. */
			usedbs = FALSE_;
			usedrq = FALSE_;
/*                    Bisection is initially turned off unless it is forced */
			needbs = ! tryrqc;
L120:
/*                    Check if bisection should be used to refine eigenvalue */
			if (needbs) {
/*                       Take the bisection as new iterate */
			    usedbs = TRUE_;
			    itmp1 = iwork[iindr + windex];
			    offset = indexw[wbegin] - 1;
			    d__1 = eps * 2.;
			    dlarrb_(&in, &d__[ibegin], &work[indlld + ibegin 
				    - 1], &indeig, &indeig, &c_b5, &d__1, &
				    offset, &work[wbegin], &wgap[wbegin], &
				    werr[wbegin], &work[indwrk], &iwork[
				    iindwk], pivmin, &spdiam, &itmp1, &iinfo);
			    if (iinfo != 0) {
				*info = -3;
				return;
			    }
			    lambda = work[windex];
/*                       Reset twist index from inaccurate LAMBDA to */
/*                       force computation of true MINGMA */
			    iwork[iindr + windex] = 0;
			}
/*                    Given LAMBDA, compute the eigenvector. */
			L__1 = ! usedbs;
			dlar1v_(&in, &c__1, &in, &lambda, &d__[ibegin], &l[
				ibegin], &work[indld + ibegin - 1], &work[
				indlld + ibegin - 1], pivmin, &gaptol, &z__[
				ibegin + windex * z_dim1], &L__1, &negcnt, &
				ztz, &mingma, &iwork[iindr + windex], &isuppz[
				(windex << 1) - 1], &nrminv, &resid, &rqcorr, 
				&work[indwrk]);
			if (iter == 0) {
			    bstres = resid;
			    bstw = lambda;
			} else if (resid < bstres) {
			    bstres = resid;
			    bstw = lambda;
			}
/* Computing MIN */
			i__4 = isupmn, i__5 = isuppz[(windex << 1) - 1];
			isupmn = f2cmin(i__4,i__5);
/* Computing MAX */
			i__4 = isupmx, i__5 = isuppz[windex * 2];
			isupmx = f2cmax(i__4,i__5);
			++iter;
/*                    sin alpha <= |resid|/gap */
/*                    Note that both the residual and the gap are */
/*                    proportional to the matrix, so ||T|| doesn't play */
/*                    a role in the quotient */

/*                    Convergence test for Rayleigh-Quotient iteration */
/*                    (omitted when Bisection has been used) */

			if (resid > tol * gap && abs(rqcorr) > rqtol * abs(
				lambda) && ! usedbs) {
/*                       We need to check that the RQCORR update doesn't */
/*                       move the eigenvalue away from the desired one and */
/*                       towards a neighbor. -> protection with bisection */
			    if (indeig <= negcnt) {
/*                          The wanted eigenvalue lies to the left */
				sgndef = -1.;
			    } else {
/*                          The wanted eigenvalue lies to the right */
				sgndef = 1.;
			    }
/*                       We only use the RQCORR if it improves the */
/*                       the iterate reasonably. */
			    if (rqcorr * sgndef >= 0. && lambda + rqcorr <= 
				    right && lambda + rqcorr >= left) {
				usedrq = TRUE_;
/*                          Store new midpoint of bisection interval in WORK */
				if (sgndef == 1.) {
/*                             The current LAMBDA is on the left of the true */
/*                             eigenvalue */
				    left = lambda;
/*                             We prefer to assume that the error estimate */
/*                             is correct. We could make the interval not */
/*                             as a bracket but to be modified if the RQCORR */
/*                             chooses to. In this case, the RIGHT side should */
/*                             be modified as follows: */
/*                              RIGHT = MAX(RIGHT, LAMBDA + RQCORR) */
				} else {
/*                             The current LAMBDA is on the right of the true */
/*                             eigenvalue */
				    right = lambda;
/*                             See comment about assuming the error estimate is */
/*                             correct above. */
/*                              LEFT = MIN(LEFT, LAMBDA + RQCORR) */
				}
				work[windex] = (right + left) * .5;
/*                          Take RQCORR since it has the correct sign and */
/*                          improves the iterate reasonably */
				lambda += rqcorr;
/*                          Update width of error interval */
				werr[windex] = (right - left) * .5;
			    } else {
				needbs = TRUE_;
			    }
			    if (right - left < rqtol * abs(lambda)) {
/*                             The eigenvalue is computed to bisection accuracy */
/*                             compute eigenvector and stop */
				usedbs = TRUE_;
				goto L120;
			    } else if (iter < 10) {
				goto L120;
			    } else if (iter == 10) {
				needbs = TRUE_;
				goto L120;
			    } else {
				*info = 5;
				return;
			    }
			} else {
			    stp2ii = FALSE_;
			    if (usedrq && usedbs && bstres <= resid) {
				lambda = bstw;
				stp2ii = TRUE_;
			    }
			    if (stp2ii) {
/*                          improve error angle by second step */
				L__1 = ! usedbs;
				dlar1v_(&in, &c__1, &in, &lambda, &d__[ibegin]
					, &l[ibegin], &work[indld + ibegin - 
					1], &work[indlld + ibegin - 1], 
					pivmin, &gaptol, &z__[ibegin + windex 
					* z_dim1], &L__1, &negcnt, &ztz, &
					mingma, &iwork[iindr + windex], &
					isuppz[(windex << 1) - 1], &nrminv, &
					resid, &rqcorr, &work[indwrk]);
			    }
			    work[windex] = lambda;
			}

/*                    Compute FP-vector support w.r.t. whole matrix */

			isuppz[(windex << 1) - 1] += oldien;
			isuppz[windex * 2] += oldien;
			zfrom = isuppz[(windex << 1) - 1];
			zto = isuppz[windex * 2];
			isupmn += oldien;
			isupmx += oldien;
/*                    Ensure vector is ok if support in the RQI has changed */
			if (isupmn < zfrom) {
			    i__4 = zfrom - 1;
			    for (ii = isupmn; ii <= i__4; ++ii) {
				z__[ii + windex * z_dim1] = 0.;
/* L122: */
			    }
			}
			if (isupmx > zto) {
			    i__4 = isupmx;
			    for (ii = zto + 1; ii <= i__4; ++ii) {
				z__[ii + windex * z_dim1] = 0.;
/* L123: */
			    }
			}
			i__4 = zto - zfrom + 1;
			dscal_(&i__4, &nrminv, &z__[zfrom + windex * z_dim1], 
				&c__1);
L125:
/*                    Update W */
			w[windex] = lambda + sigma;
/*                    Recompute the gaps on the left and right */
/*                    But only allow them to become larger and not */
/*                    smaller (which can only happen through "bad" */
/*                    cancellation and doesn't reflect the theory */
/*                    where the initial gaps are underestimated due */
/*                    to WERR being too crude.) */
			if (! eskip) {
			    if (k > 1) {
/* Computing MAX */
				d__1 = wgap[windmn], d__2 = w[windex] - werr[
					windex] - w[windmn] - werr[windmn];
				wgap[windmn] = f2cmax(d__1,d__2);
			    }
			    if (windex < wend) {
/* Computing MAX */
				d__1 = savgap, d__2 = w[windpl] - werr[windpl]
					 - w[windex] - werr[windex];
				wgap[windex] = f2cmax(d__1,d__2);
			    }
			}
			++idone;
		    }
/*                 here ends the code for the current child */

L139:
/*                 Proceed to any remaining child nodes */
		    newfst = j + 1;
L140:
		    ;
		}
/* L150: */
	    }
	    ++ndepth;
	    goto L40;
	}
	ibegin = iend + 1;
	wbegin = wend + 1;
L170:
	;
    }

    return;

/*     End of DLARRV */

} /* dlarrv_ */