OpenBLAS/lapack-netlib/SRC/dlarre.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 blasint logical;

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++ */


#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__2 = 2;

/* > \brief \b DLARRE given the tridiagonal matrix T, sets small off-diagonal elements to zero and for each un
reduced block Ti, finds base representations and eigenvalues. */

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

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

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

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

/*       SUBROUTINE DLARRE( RANGE, N, VL, VU, IL, IU, D, E, E2, */
/*                           RTOL1, RTOL2, SPLTOL, NSPLIT, ISPLIT, M, */
/*                           W, WERR, WGAP, IBLOCK, INDEXW, GERS, PIVMIN, */
/*                           WORK, IWORK, INFO ) */

/*       CHARACTER          RANGE */
/*       INTEGER            IL, INFO, IU, M, N, NSPLIT */
/*       DOUBLE PRECISION  PIVMIN, RTOL1, RTOL2, SPLTOL, VL, VU */
/*       INTEGER            IBLOCK( * ), ISPLIT( * ), IWORK( * ), */
/*      $                   INDEXW( * ) */
/*       DOUBLE PRECISION   D( * ), E( * ), E2( * ), GERS( * ), */
/*      $                   W( * ),WERR( * ), WGAP( * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > To find the desired eigenvalues of a given real symmetric */
/* > tridiagonal matrix T, DLARRE sets any "small" off-diagonal */
/* > elements to zero, and for each unreduced block T_i, it finds */
/* > (a) a suitable shift at one end of the block's spectrum, */
/* > (b) the base representation, T_i - sigma_i I = L_i D_i L_i^T, and */
/* > (c) eigenvalues of each L_i D_i L_i^T. */
/* > The representations and eigenvalues found are then used by */
/* > DSTEMR to compute the eigenvectors of T. */
/* > The accuracy varies depending on whether bisection is used to */
/* > find a few eigenvalues or the dqds algorithm (subroutine DLASQ2) to */
/* > conpute all and then discard any unwanted one. */
/* > As an added benefit, DLARRE also outputs the n */
/* > Gerschgorin intervals for the matrices L_i D_i L_i^T. */
/* > \endverbatim */

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

/* > \param[in] RANGE */
/* > \verbatim */
/* >          RANGE is CHARACTER*1 */
/* >          = 'A': ("All")   all eigenvalues will be found. */
/* >          = 'V': ("Value") all eigenvalues in the half-open interval */
/* >                           (VL, VU] will be found. */
/* >          = 'I': ("Index") the IL-th through IU-th eigenvalues (of the */
/* >                           entire matrix) will be found. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix. N > 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] VL */
/* > \verbatim */
/* >          VL is DOUBLE PRECISION */
/* >          If RANGE='V', the lower bound for the eigenvalues. */
/* >          Eigenvalues less than or equal to VL, or greater than VU, */
/* >          will not be returned.  VL < VU. */
/* >          If RANGE='I' or ='A', DLARRE computes bounds on the desired */
/* >          part of the spectrum. */
/* > \endverbatim */
/* > */
/* > \param[in,out] VU */
/* > \verbatim */
/* >          VU is DOUBLE PRECISION */
/* >          If RANGE='V', the upper bound for the eigenvalues. */
/* >          Eigenvalues less than or equal to VL, or greater than VU, */
/* >          will not be returned.  VL < VU. */
/* >          If RANGE='I' or ='A', DLARRE computes bounds on the desired */
/* >          part of the spectrum. */
/* > \endverbatim */
/* > */
/* > \param[in] IL */
/* > \verbatim */
/* >          IL is INTEGER */
/* >          If RANGE='I', the index of the */
/* >          smallest eigenvalue to be returned. */
/* >          1 <= IL <= IU <= N. */
/* > \endverbatim */
/* > */
/* > \param[in] IU */
/* > \verbatim */
/* >          IU is INTEGER */
/* >          If RANGE='I', the index of the */
/* >          largest eigenvalue to be returned. */
/* >          1 <= IL <= IU <= N. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* >          D is DOUBLE PRECISION array, dimension (N) */
/* >          On entry, the N diagonal elements of the tridiagonal */
/* >          matrix T. */
/* >          On exit, the N diagonal elements of the diagonal */
/* >          matrices D_i. */
/* > \endverbatim */
/* > */
/* > \param[in,out] E */
/* > \verbatim */
/* >          E is DOUBLE PRECISION array, dimension (N) */
/* >          On entry, the first (N-1) entries contain the subdiagonal */
/* >          elements of the tridiagonal matrix T; E(N) need not be set. */
/* >          On exit, E contains the subdiagonal elements of the unit */
/* >          bidiagonal matrices L_i. The entries E( ISPLIT( I ) ), */
/* >          1 <= I <= NSPLIT, contain the base points sigma_i on output. */
/* > \endverbatim */
/* > */
/* > \param[in,out] E2 */
/* > \verbatim */
/* >          E2 is DOUBLE PRECISION array, dimension (N) */
/* >          On entry, the first (N-1) entries contain the SQUARES of the */
/* >          subdiagonal elements of the tridiagonal matrix T; */
/* >          E2(N) need not be set. */
/* >          On exit, the entries E2( ISPLIT( I ) ), */
/* >          1 <= I <= NSPLIT, have been set to zero */
/* > \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] SPLTOL */
/* > \verbatim */
/* >          SPLTOL is DOUBLE PRECISION */
/* >          The threshold for splitting. */
/* > \endverbatim */
/* > */
/* > \param[out] NSPLIT */
/* > \verbatim */
/* >          NSPLIT is INTEGER */
/* >          The number of blocks T splits into. 1 <= NSPLIT <= N. */
/* > \endverbatim */
/* > */
/* > \param[out] 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., and the NSPLIT-th consists of rows/columns */
/* >          ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. */
/* > \endverbatim */
/* > */
/* > \param[out] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The total number of eigenvalues (of all L_i D_i L_i^T) */
/* >          found. */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* >          W is DOUBLE PRECISION array, dimension (N) */
/* >          The first M elements contain the eigenvalues. The */
/* >          eigenvalues of each of the blocks, L_i D_i L_i^T, are */
/* >          sorted in ascending order ( DLARRE may use the */
/* >          remaining N-M elements as workspace). */
/* > \endverbatim */
/* > */
/* > \param[out] WERR */
/* > \verbatim */
/* >          WERR is DOUBLE PRECISION array, dimension (N) */
/* >          The error bound on the corresponding eigenvalue in W. */
/* > \endverbatim */
/* > */
/* > \param[out] WGAP */
/* > \verbatim */
/* >          WGAP is DOUBLE PRECISION array, dimension (N) */
/* >          The separation from the right neighbor eigenvalue in W. */
/* >          The gap is only with respect to the eigenvalues of the same block */
/* >          as each block has its own representation tree. */
/* >          Exception: at the right end of a block we store the left gap */
/* > \endverbatim */
/* > */
/* > \param[out] 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[out] 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 block 2 */
/* > \endverbatim */
/* > */
/* > \param[out] 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)). */
/* > \endverbatim */
/* > */
/* > \param[out] PIVMIN */
/* > \verbatim */
/* >          PIVMIN is DOUBLE PRECISION */
/* >          The minimum pivot in the Sturm sequence for T. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is DOUBLE PRECISION array, dimension (6*N) */
/* >          Workspace. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (5*N) */
/* >          Workspace. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit */
/* >          > 0:  A problem occurred in DLARRE. */
/* >          < 0:  One of the called subroutines signaled an internal problem. */
/* >                Needs inspection of the corresponding parameter IINFO */
/* >                for further information. */
/* > */
/* >          =-1:  Problem in DLARRD. */
/* >          = 2:  No base representation could be found in MAXTRY iterations. */
/* >                Increasing MAXTRY and recompilation might be a remedy. */
/* >          =-3:  Problem in DLARRB when computing the refined root */
/* >                representation for DLASQ2. */
/* >          =-4:  Problem in DLARRB when preforming bisection on the */
/* >                desired part of the spectrum. */
/* >          =-5:  Problem in DLASQ2. */
/* >          =-6:  Problem in DLASQ2. */
/* > \endverbatim */

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

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

/* > \date June 2016 */

/* > \ingroup OTHERauxiliary */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  The base representations are required to suffer very little */
/* >  element growth and consequently define all their eigenvalues to */
/* >  high relative accuracy. */
/* > \endverbatim */

/* > \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 \n */
/* > */
/*  ===================================================================== */
/* Subroutine */ void dlarre_(char *range, integer *n, doublereal *vl, 
	doublereal *vu, integer *il, integer *iu, doublereal *d__, doublereal 
	*e, doublereal *e2, doublereal *rtol1, doublereal *rtol2, doublereal *
	spltol, integer *nsplit, integer *isplit, integer *m, doublereal *w, 
	doublereal *werr, doublereal *wgap, integer *iblock, integer *indexw, 
	doublereal *gers, doublereal *pivmin, doublereal *work, integer *
	iwork, integer *info)
{
    /* System generated locals */
    integer i__1, i__2;
    doublereal d__1, d__2, d__3;

    /* Local variables */
    doublereal eabs;
    integer iend, jblk;
    doublereal eold;
    integer indl;
    doublereal dmax__, emax;
    integer wend, idum, indu;
    doublereal rtol;
    integer i__, j, iseed[4];
    doublereal avgap, sigma;
    extern logical lsame_(char *, char *);
    integer iinfo;
    extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    logical norep;
    doublereal s1, s2;
    extern /* Subroutine */ void dlasq2_(integer *, doublereal *, integer *);
    integer mb;
    doublereal gl;
    integer in;
    extern doublereal dlamch_(char *);
    integer mm;
    doublereal gu;
    integer ibegin;
    logical forceb;
    integer irange;
    doublereal sgndef;
    extern /* Subroutine */ void dlarra_(integer *, doublereal *, doublereal *,
	     doublereal *, doublereal *, doublereal *, integer *, integer *, 
	    integer *), dlarrb_(integer *, doublereal *, doublereal *, 
	    integer *, integer *, doublereal *, doublereal *, integer *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, integer *,
	     doublereal *, doublereal *, integer *, integer *), dlarrc_(char *
	    , integer *, doublereal *, doublereal *, doublereal *, doublereal 
	    *, doublereal *, integer *, integer *, integer *, integer *);
    integer wbegin;
    doublereal safmin, spdiam;
    extern /* Subroutine */ void dlarrd_(char *, char *, integer *, doublereal 
	    *, doublereal *, integer *, integer *, doublereal *, doublereal *,
	     doublereal *, doublereal *, doublereal *, doublereal *, integer *
	    , integer *, integer *, doublereal *, doublereal *, doublereal *, 
	    doublereal *, integer *, integer *, doublereal *, integer *, 
	    integer *), dlarrk_(integer *, integer *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, integer *)
	    ;
    logical usedqd;
    doublereal clwdth, isleft;
    extern /* Subroutine */ void dlarnv_(integer *, integer *, integer *, 
	    doublereal *);
    doublereal isrght, bsrtol, dpivot;
    integer cnt;
    doublereal eps, tau, tmp, rtl;
    integer cnt1, cnt2;
    doublereal tmp1;


/*  -- 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 */
    --iwork;
    --work;
    --gers;
    --indexw;
    --iblock;
    --wgap;
    --werr;
    --w;
    --isplit;
    --e2;
    --e;
    --d__;

    /* Function Body */
    *info = 0;

/*     Quick return if possible */

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

/*     Decode RANGE */

    if (lsame_(range, "A")) {
	irange = 1;
    } else if (lsame_(range, "V")) {
	irange = 3;
    } else if (lsame_(range, "I")) {
	irange = 2;
    }
    *m = 0;
/*     Get machine constants */
    safmin = dlamch_("S");
    eps = dlamch_("P");
/*     Set parameters */
    rtl = sqrt(eps);
    bsrtol = sqrt(eps);
/*     Treat case of 1x1 matrix for quick return */
    if (*n == 1) {
	if (irange == 1 || irange == 3 && d__[1] > *vl && d__[1] <= *vu || 
		irange == 2 && *il == 1 && *iu == 1) {
	    *m = 1;
	    w[1] = d__[1];
/*           The computation error of the eigenvalue is zero */
	    werr[1] = 0.;
	    wgap[1] = 0.;
	    iblock[1] = 1;
	    indexw[1] = 1;
	    gers[1] = d__[1];
	    gers[2] = d__[1];
	}
/*        store the shift for the initial RRR, which is zero in this case */
	e[1] = 0.;
	return;
    }
/*     General case: tridiagonal matrix of order > 1 */

/*     Init WERR, WGAP. Compute Gerschgorin intervals and spectral diameter. */
/*     Compute maximum off-diagonal entry and pivmin. */
    gl = d__[1];
    gu = d__[1];
    eold = 0.;
    emax = 0.;
    e[*n] = 0.;
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
	werr[i__] = 0.;
	wgap[i__] = 0.;
	eabs = (d__1 = e[i__], abs(d__1));
	if (eabs >= emax) {
	    emax = eabs;
	}
	tmp1 = eabs + eold;
	gers[(i__ << 1) - 1] = d__[i__] - tmp1;
/* Computing MIN */
	d__1 = gl, d__2 = gers[(i__ << 1) - 1];
	gl = f2cmin(d__1,d__2);
	gers[i__ * 2] = d__[i__] + tmp1;
/* Computing MAX */
	d__1 = gu, d__2 = gers[i__ * 2];
	gu = f2cmax(d__1,d__2);
	eold = eabs;
/* L5: */
    }
/*     The minimum pivot allowed in the Sturm sequence for T */
/* Computing MAX */
/* Computing 2nd power */
    d__3 = emax;
    d__1 = 1., d__2 = d__3 * d__3;
    *pivmin = safmin * f2cmax(d__1,d__2);
/*     Compute spectral diameter. The Gerschgorin bounds give an */
/*     estimate that is wrong by at most a factor of SQRT(2) */
    spdiam = gu - gl;
/*     Compute splitting points */
    dlarra_(n, &d__[1], &e[1], &e2[1], spltol, &spdiam, nsplit, &isplit[1], &
	    iinfo);
/*     Can force use of bisection instead of faster DQDS. */
/*     Option left in the code for future multisection work. */
    forceb = FALSE_;
/*     Initialize USEDQD, DQDS should be used for ALLRNG unless someone */
/*     explicitly wants bisection. */
    usedqd = irange == 1 && ! forceb;
    if (irange == 1 && ! forceb) {
/*        Set interval [VL,VU] that contains all eigenvalues */
	*vl = gl;
	*vu = gu;
    } else {
/*        We call DLARRD to find crude approximations to the eigenvalues */
/*        in the desired range. In case IRANGE = INDRNG, we also obtain the */
/*        interval (VL,VU] that contains all the wanted eigenvalues. */
/*        An interval [LEFT,RIGHT] has converged if */
/*        RIGHT-LEFT.LT.RTOL*MAX(ABS(LEFT),ABS(RIGHT)) */
/*        DLARRD needs a WORK of size 4*N, IWORK of size 3*N */
	dlarrd_(range, "B", n, vl, vu, il, iu, &gers[1], &bsrtol, &d__[1], &e[
		1], &e2[1], pivmin, nsplit, &isplit[1], &mm, &w[1], &werr[1], 
		vl, vu, &iblock[1], &indexw[1], &work[1], &iwork[1], &iinfo);
	if (iinfo != 0) {
	    *info = -1;
	    return;
	}
/*        Make sure that the entries M+1 to N in W, WERR, IBLOCK, INDEXW are 0 */
	i__1 = *n;
	for (i__ = mm + 1; i__ <= i__1; ++i__) {
	    w[i__] = 0.;
	    werr[i__] = 0.;
	    iblock[i__] = 0;
	    indexw[i__] = 0;
/* L14: */
	}
    }
/* ** */
/*     Loop over unreduced blocks */
    ibegin = 1;
    wbegin = 1;
    i__1 = *nsplit;
    for (jblk = 1; jblk <= i__1; ++jblk) {
	iend = isplit[jblk];
	in = iend - ibegin + 1;
/*        1 X 1 block */
	if (in == 1) {
	    if (irange == 1 || irange == 3 && d__[ibegin] > *vl && d__[ibegin]
		     <= *vu || irange == 2 && iblock[wbegin] == jblk) {
		++(*m);
		w[*m] = d__[ibegin];
		werr[*m] = 0.;
/*              The gap for a single block doesn't matter for the later */
/*              algorithm and is assigned an arbitrary large value */
		wgap[*m] = 0.;
		iblock[*m] = jblk;
		indexw[*m] = 1;
		++wbegin;
	    }
/*           E( IEND ) holds the shift for the initial RRR */
	    e[iend] = 0.;
	    ibegin = iend + 1;
	    goto L170;
	}

/*        Blocks of size larger than 1x1 */

/*        E( IEND ) will hold the shift for the initial RRR, for now set it =0 */
	e[iend] = 0.;

/*        Find local outer bounds GL,GU for the block */
	gl = d__[ibegin];
	gu = d__[ibegin];
	i__2 = iend;
	for (i__ = ibegin; 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);
/* L15: */
	}
	spdiam = gu - gl;
	if (! (irange == 1 && ! forceb)) {
/*           Count the number of eigenvalues in the current block. */
	    mb = 0;
	    i__2 = mm;
	    for (i__ = wbegin; i__ <= i__2; ++i__) {
		if (iblock[i__] == jblk) {
		    ++mb;
		} else {
		    goto L21;
		}
/* L20: */
	    }
L21:
	    if (mb == 0) {
/*              No eigenvalue in the current block lies in the desired range */
/*              E( IEND ) holds the shift for the initial RRR */
		e[iend] = 0.;
		ibegin = iend + 1;
		goto L170;
	    } else {
/*              Decide whether dqds or bisection is more efficient */
		usedqd = (doublereal) mb > in * .5 && ! forceb;
		wend = wbegin + mb - 1;
/*              Calculate gaps for the current block */
/*              In later stages, when representations for individual */
/*              eigenvalues are different, we use SIGMA = E( IEND ). */
		sigma = 0.;
		i__2 = wend - 1;
		for (i__ = wbegin; i__ <= i__2; ++i__) {
/* Computing MAX */
		    d__1 = 0., d__2 = w[i__ + 1] - werr[i__ + 1] - (w[i__] + 
			    werr[i__]);
		    wgap[i__] = f2cmax(d__1,d__2);
/* L30: */
		}
/* Computing MAX */
		d__1 = 0., d__2 = *vu - sigma - (w[wend] + werr[wend]);
		wgap[wend] = f2cmax(d__1,d__2);
/*              Find local index of the first and last desired evalue. */
		indl = indexw[wbegin];
		indu = indexw[wend];
	    }
	}
	if (irange == 1 && ! forceb || usedqd) {
/*           Case of DQDS */
/*           Find approximations to the extremal eigenvalues of the block */
	    dlarrk_(&in, &c__1, &gl, &gu, &d__[ibegin], &e2[ibegin], pivmin, &
		    rtl, &tmp, &tmp1, &iinfo);
	    if (iinfo != 0) {
		*info = -1;
		return;
	    }
/* Computing MAX */
	    d__2 = gl, d__3 = tmp - tmp1 - eps * 100. * (d__1 = tmp - tmp1, 
		    abs(d__1));
	    isleft = f2cmax(d__2,d__3);
	    dlarrk_(&in, &in, &gl, &gu, &d__[ibegin], &e2[ibegin], pivmin, &
		    rtl, &tmp, &tmp1, &iinfo);
	    if (iinfo != 0) {
		*info = -1;
		return;
	    }
/* Computing MIN */
	    d__2 = gu, d__3 = tmp + tmp1 + eps * 100. * (d__1 = tmp + tmp1, 
		    abs(d__1));
	    isrght = f2cmin(d__2,d__3);
/*           Improve the estimate of the spectral diameter */
	    spdiam = isrght - isleft;
	} else {
/*           Case of bisection */
/*           Find approximations to the wanted extremal eigenvalues */
/* Computing MAX */
	    d__2 = gl, d__3 = w[wbegin] - werr[wbegin] - eps * 100. * (d__1 = 
		    w[wbegin] - werr[wbegin], abs(d__1));
	    isleft = f2cmax(d__2,d__3);
/* Computing MIN */
	    d__2 = gu, d__3 = w[wend] + werr[wend] + eps * 100. * (d__1 = w[
		    wend] + werr[wend], abs(d__1));
	    isrght = f2cmin(d__2,d__3);
	}
/*        Decide whether the base representation for the current block */
/*        L_JBLK D_JBLK L_JBLK^T = T_JBLK - sigma_JBLK I */
/*        should be on the left or the right end of the current block. */
/*        The strategy is to shift to the end which is "more populated" */
/*        Furthermore, decide whether to use DQDS for the computation of */
/*        the eigenvalue approximations at the end of DLARRE or bisection. */
/*        dqds is chosen if all eigenvalues are desired or the number of */
/*        eigenvalues to be computed is large compared to the blocksize. */
	if (irange == 1 && ! forceb) {
/*           If all the eigenvalues have to be computed, we use dqd */
	    usedqd = TRUE_;
/*           INDL is the local index of the first eigenvalue to compute */
	    indl = 1;
	    indu = in;
/*           MB =  number of eigenvalues to compute */
	    mb = in;
	    wend = wbegin + mb - 1;
/*           Define 1/4 and 3/4 points of the spectrum */
	    s1 = isleft + spdiam * .25;
	    s2 = isrght - spdiam * .25;
	} else {
/*           DLARRD has computed IBLOCK and INDEXW for each eigenvalue */
/*           approximation. */
/*           choose sigma */
	    if (usedqd) {
		s1 = isleft + spdiam * .25;
		s2 = isrght - spdiam * .25;
	    } else {
		tmp = f2cmin(isrght,*vu) - f2cmax(isleft,*vl);
		s1 = f2cmax(isleft,*vl) + tmp * .25;
		s2 = f2cmin(isrght,*vu) - tmp * .25;
	    }
	}
/*        Compute the negcount at the 1/4 and 3/4 points */
	if (mb > 1) {
	    dlarrc_("T", &in, &s1, &s2, &d__[ibegin], &e[ibegin], pivmin, &
		    cnt, &cnt1, &cnt2, &iinfo);
	}
	if (mb == 1) {
	    sigma = gl;
	    sgndef = 1.;
	} else if (cnt1 - indl >= indu - cnt2) {
	    if (irange == 1 && ! forceb) {
		sigma = f2cmax(isleft,gl);
	    } else if (usedqd) {
/*              use Gerschgorin bound as shift to get pos def matrix */
/*              for dqds */
		sigma = isleft;
	    } else {
/*              use approximation of the first desired eigenvalue of the */
/*              block as shift */
		sigma = f2cmax(isleft,*vl);
	    }
	    sgndef = 1.;
	} else {
	    if (irange == 1 && ! forceb) {
		sigma = f2cmin(isrght,gu);
	    } else if (usedqd) {
/*              use Gerschgorin bound as shift to get neg def matrix */
/*              for dqds */
		sigma = isrght;
	    } else {
/*              use approximation of the first desired eigenvalue of the */
/*              block as shift */
		sigma = f2cmin(isrght,*vu);
	    }
	    sgndef = -1.;
	}
/*        An initial SIGMA has been chosen that will be used for computing */
/*        T - SIGMA I = L D L^T */
/*        Define the increment TAU of the shift in case the initial shift */
/*        needs to be refined to obtain a factorization with not too much */
/*        element growth. */
	if (usedqd) {
/*           The initial SIGMA was to the outer end of the spectrum */
/*           the matrix is definite and we need not retreat. */
	    tau = spdiam * eps * *n + *pivmin * 2.;
/* Computing MAX */
	    d__1 = tau, d__2 = eps * 2. * abs(sigma);
	    tau = f2cmax(d__1,d__2);
	} else {
	    if (mb > 1) {
		clwdth = w[wend] + werr[wend] - w[wbegin] - werr[wbegin];
		avgap = (d__1 = clwdth / (doublereal) (wend - wbegin), abs(
			d__1));
		if (sgndef == 1.) {
/* Computing MAX */
		    d__1 = wgap[wbegin];
		    tau = f2cmax(d__1,avgap) * .5;
/* Computing MAX */
		    d__1 = tau, d__2 = werr[wbegin];
		    tau = f2cmax(d__1,d__2);
		} else {
/* Computing MAX */
		    d__1 = wgap[wend - 1];
		    tau = f2cmax(d__1,avgap) * .5;
/* Computing MAX */
		    d__1 = tau, d__2 = werr[wend];
		    tau = f2cmax(d__1,d__2);
		}
	    } else {
		tau = werr[wbegin];
	    }
	}

	for (idum = 1; idum <= 6; ++idum) {
/*           Compute L D L^T factorization of tridiagonal matrix T - sigma I. */
/*           Store D in WORK(1:IN), L in WORK(IN+1:2*IN), and reciprocals of */
/*           pivots in WORK(2*IN+1:3*IN) */
	    dpivot = d__[ibegin] - sigma;
	    work[1] = dpivot;
	    dmax__ = abs(work[1]);
	    j = ibegin;
	    i__2 = in - 1;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		work[(in << 1) + i__] = 1. / work[i__];
		tmp = e[j] * work[(in << 1) + i__];
		work[in + i__] = tmp;
		dpivot = d__[j + 1] - sigma - tmp * e[j];
		work[i__ + 1] = dpivot;
/* Computing MAX */
		d__1 = dmax__, d__2 = abs(dpivot);
		dmax__ = f2cmax(d__1,d__2);
		++j;
/* L70: */
	    }
/*           check for element growth */
	    if (dmax__ > spdiam * 64.) {
		norep = TRUE_;
	    } else {
		norep = FALSE_;
	    }
	    if (usedqd && ! norep) {
/*              Ensure the definiteness of the representation */
/*              All entries of D (of L D L^T) must have the same sign */
		i__2 = in;
		for (i__ = 1; i__ <= i__2; ++i__) {
		    tmp = sgndef * work[i__];
		    if (tmp < 0.) {
			norep = TRUE_;
		    }
/* L71: */
		}
	    }
	    if (norep) {
/*              Note that in the case of IRANGE=ALLRNG, we use the Gerschgorin */
/*              shift which makes the matrix definite. So we should end up */
/*              here really only in the case of IRANGE = VALRNG or INDRNG. */
		if (idum == 5) {
		    if (sgndef == 1.) {
/*                    The fudged Gerschgorin shift should succeed */
			sigma = gl - spdiam * 2. * eps * *n - *pivmin * 4.;
		    } else {
			sigma = gu + spdiam * 2. * eps * *n + *pivmin * 4.;
		    }
		} else {
		    sigma -= sgndef * tau;
		    tau *= 2.;
		}
	    } else {
/*              an initial RRR is found */
		goto L83;
	    }
/* L80: */
	}
/*        if the program reaches this point, no base representation could be */
/*        found in MAXTRY iterations. */
	*info = 2;
	return;
L83:
/*        At this point, we have found an initial base representation */
/*        T - SIGMA I = L D L^T with not too much element growth. */
/*        Store the shift. */
	e[iend] = sigma;
/*        Store D and L. */
	dcopy_(&in, &work[1], &c__1, &d__[ibegin], &c__1);
	i__2 = in - 1;
	dcopy_(&i__2, &work[in + 1], &c__1, &e[ibegin], &c__1);
	if (mb > 1) {

/*           Perturb each entry of the base representation by a small */
/*           (but random) relative amount to overcome difficulties with */
/*           glued matrices. */

	    for (i__ = 1; i__ <= 4; ++i__) {
		iseed[i__ - 1] = 1;
/* L122: */
	    }
	    i__2 = (in << 1) - 1;
	    dlarnv_(&c__2, iseed, &i__2, &work[1]);
	    i__2 = in - 1;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		d__[ibegin + i__ - 1] *= eps * 8. * work[i__] + 1.;
		e[ibegin + i__ - 1] *= eps * 8. * work[in + i__] + 1.;
/* L125: */
	    }
	    d__[iend] *= eps * 4. * work[in] + 1.;

	}

/*        Don't update the Gerschgorin intervals because keeping track */
/*        of the updates would be too much work in DLARRV. */
/*        We update W instead and use it to locate the proper Gerschgorin */
/*        intervals. */
/*        Compute the required eigenvalues of L D L' by bisection or dqds */
	if (! usedqd) {
/*           If DLARRD has been used, shift the eigenvalue approximations */
/*           according to their representation. This is necessary for */
/*           a uniform DLARRV since dqds computes eigenvalues of the */
/*           shifted representation. In DLARRV, W will always hold the */
/*           UNshifted eigenvalue approximation. */
	    i__2 = wend;
	    for (j = wbegin; j <= i__2; ++j) {
		w[j] -= sigma;
		werr[j] += (d__1 = w[j], abs(d__1)) * eps;
/* L134: */
	    }
/*           call DLARRB to reduce eigenvalue error of the approximations */
/*           from DLARRD */
	    i__2 = iend - 1;
	    for (i__ = ibegin; i__ <= i__2; ++i__) {
/* Computing 2nd power */
		d__1 = e[i__];
		work[i__] = d__[i__] * (d__1 * d__1);
/* L135: */
	    }
/*           use bisection to find EV from INDL to INDU */
	    i__2 = indl - 1;
	    dlarrb_(&in, &d__[ibegin], &work[ibegin], &indl, &indu, rtol1, 
		    rtol2, &i__2, &w[wbegin], &wgap[wbegin], &werr[wbegin], &
		    work[(*n << 1) + 1], &iwork[1], pivmin, &spdiam, &in, &
		    iinfo);
	    if (iinfo != 0) {
		*info = -4;
		return;
	    }
/*           DLARRB computes all gaps correctly except for the last one */
/*           Record distance to VU/GU */
/* Computing MAX */
	    d__1 = 0., d__2 = *vu - sigma - (w[wend] + werr[wend]);
	    wgap[wend] = f2cmax(d__1,d__2);
	    i__2 = indu;
	    for (i__ = indl; i__ <= i__2; ++i__) {
		++(*m);
		iblock[*m] = jblk;
		indexw[*m] = i__;
/* L138: */
	    }
	} else {
/*           Call dqds to get all eigs (and then possibly delete unwanted */
/*           eigenvalues). */
/*           Note that dqds finds the eigenvalues of the L D L^T representation */
/*           of T to high relative accuracy. High relative accuracy */
/*           might be lost when the shift of the RRR is subtracted to obtain */
/*           the eigenvalues of T. However, T is not guaranteed to define its */
/*           eigenvalues to high relative accuracy anyway. */
/*           Set RTOL to the order of the tolerance used in DLASQ2 */
/*           This is an ESTIMATED error, the worst case bound is 4*N*EPS */
/*           which is usually too large and requires unnecessary work to be */
/*           done by bisection when computing the eigenvectors */
	    rtol = log((doublereal) in) * 4. * eps;
	    j = ibegin;
	    i__2 = in - 1;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		work[(i__ << 1) - 1] = (d__1 = d__[j], abs(d__1));
		work[i__ * 2] = e[j] * e[j] * work[(i__ << 1) - 1];
		++j;
/* L140: */
	    }
	    work[(in << 1) - 1] = (d__1 = d__[iend], abs(d__1));
	    work[in * 2] = 0.;
	    dlasq2_(&in, &work[1], &iinfo);
	    if (iinfo != 0) {
/*              If IINFO = -5 then an index is part of a tight cluster */
/*              and should be changed. The index is in IWORK(1) and the */
/*              gap is in WORK(N+1) */
		*info = -5;
		return;
	    } else {
/*              Test that all eigenvalues are positive as expected */
		i__2 = in;
		for (i__ = 1; i__ <= i__2; ++i__) {
		    if (work[i__] < 0.) {
			*info = -6;
			return;
		    }
/* L149: */
		}
	    }
	    if (sgndef > 0.) {
		i__2 = indu;
		for (i__ = indl; i__ <= i__2; ++i__) {
		    ++(*m);
		    w[*m] = work[in - i__ + 1];
		    iblock[*m] = jblk;
		    indexw[*m] = i__;
/* L150: */
		}
	    } else {
		i__2 = indu;
		for (i__ = indl; i__ <= i__2; ++i__) {
		    ++(*m);
		    w[*m] = -work[i__];
		    iblock[*m] = jblk;
		    indexw[*m] = i__;
/* L160: */
		}
	    }
	    i__2 = *m;
	    for (i__ = *m - mb + 1; i__ <= i__2; ++i__) {
/*              the value of RTOL below should be the tolerance in DLASQ2 */
		werr[i__] = rtol * (d__1 = w[i__], abs(d__1));
/* L165: */
	    }
	    i__2 = *m - 1;
	    for (i__ = *m - mb + 1; i__ <= i__2; ++i__) {
/*              compute the right gap between the intervals */
/* Computing MAX */
		d__1 = 0., d__2 = w[i__ + 1] - werr[i__ + 1] - (w[i__] + werr[
			i__]);
		wgap[i__] = f2cmax(d__1,d__2);
/* L166: */
	    }
/* Computing MAX */
	    d__1 = 0., d__2 = *vu - sigma - (w[*m] + werr[*m]);
	    wgap[*m] = f2cmax(d__1,d__2);
	}
/*        proceed with next block */
	ibegin = iend + 1;
	wbegin = wend + 1;
L170:
	;
    }

    return;

/*     end of DLARRE */

} /* dlarre_ */