OpenBLAS/lapack-netlib/SRC/clar1v.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)
*/




/* > \brief \b CLAR1V computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn 
of the tridiagonal matrix LDLT - λI. */

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

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

/* > \htmlonly */
/* > Download CLAR1V + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clar1v.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clar1v.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clar1v.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

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

/*       SUBROUTINE CLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD, */
/*                  PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, */
/*                  R, ISUPPZ, NRMINV, RESID, RQCORR, WORK ) */

/*       LOGICAL            WANTNC */
/*       INTEGER   B1, BN, N, NEGCNT, R */
/*       REAL               GAPTOL, LAMBDA, MINGMA, NRMINV, PIVMIN, RESID, */
/*      $                   RQCORR, ZTZ */
/*       INTEGER            ISUPPZ( * ) */
/*       REAL               D( * ), L( * ), LD( * ), LLD( * ), */
/*      $                  WORK( * ) */
/*       COMPLEX          Z( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > CLAR1V computes the (scaled) r-th column of the inverse of */
/* > the sumbmatrix in rows B1 through BN of the tridiagonal matrix */
/* > L D L**T - sigma I. When sigma is close to an eigenvalue, the */
/* > computed vector is an accurate eigenvector. Usually, r corresponds */
/* > to the index where the eigenvector is largest in magnitude. */
/* > The following steps accomplish this computation : */
/* > (a) Stationary qd transform,  L D L**T - sigma I = L(+) D(+) L(+)**T, */
/* > (b) Progressive qd transform, L D L**T - sigma I = U(-) D(-) U(-)**T, */
/* > (c) Computation of the diagonal elements of the inverse of */
/* >     L D L**T - sigma I by combining the above transforms, and choosing */
/* >     r as the index where the diagonal of the inverse is (one of the) */
/* >     largest in magnitude. */
/* > (d) Computation of the (scaled) r-th column of the inverse using the */
/* >     twisted factorization obtained by combining the top part of the */
/* >     the stationary and the bottom part of the progressive transform. */
/* > \endverbatim */

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

/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >           The order of the matrix L D L**T. */
/* > \endverbatim */
/* > */
/* > \param[in] B1 */
/* > \verbatim */
/* >          B1 is INTEGER */
/* >           First index of the submatrix of L D L**T. */
/* > \endverbatim */
/* > */
/* > \param[in] BN */
/* > \verbatim */
/* >          BN is INTEGER */
/* >           Last index of the submatrix of L D L**T. */
/* > \endverbatim */
/* > */
/* > \param[in] LAMBDA */
/* > \verbatim */
/* >          LAMBDA is REAL */
/* >           The shift. In order to compute an accurate eigenvector, */
/* >           LAMBDA should be a good approximation to an eigenvalue */
/* >           of L D L**T. */
/* > \endverbatim */
/* > */
/* > \param[in] L */
/* > \verbatim */
/* >          L is REAL array, dimension (N-1) */
/* >           The (n-1) subdiagonal elements of the unit bidiagonal matrix */
/* >           L, in elements 1 to N-1. */
/* > \endverbatim */
/* > */
/* > \param[in] D */
/* > \verbatim */
/* >          D is REAL array, dimension (N) */
/* >           The n diagonal elements of the diagonal matrix D. */
/* > \endverbatim */
/* > */
/* > \param[in] LD */
/* > \verbatim */
/* >          LD is REAL array, dimension (N-1) */
/* >           The n-1 elements L(i)*D(i). */
/* > \endverbatim */
/* > */
/* > \param[in] LLD */
/* > \verbatim */
/* >          LLD is REAL array, dimension (N-1) */
/* >           The n-1 elements L(i)*L(i)*D(i). */
/* > \endverbatim */
/* > */
/* > \param[in] PIVMIN */
/* > \verbatim */
/* >          PIVMIN is REAL */
/* >           The minimum pivot in the Sturm sequence. */
/* > \endverbatim */
/* > */
/* > \param[in] GAPTOL */
/* > \verbatim */
/* >          GAPTOL is REAL */
/* >           Tolerance that indicates when eigenvector entries are negligible */
/* >           w.r.t. their contribution to the residual. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Z */
/* > \verbatim */
/* >          Z is COMPLEX array, dimension (N) */
/* >           On input, all entries of Z must be set to 0. */
/* >           On output, Z contains the (scaled) r-th column of the */
/* >           inverse. The scaling is such that Z(R) equals 1. */
/* > \endverbatim */
/* > */
/* > \param[in] WANTNC */
/* > \verbatim */
/* >          WANTNC is LOGICAL */
/* >           Specifies whether NEGCNT has to be computed. */
/* > \endverbatim */
/* > */
/* > \param[out] NEGCNT */
/* > \verbatim */
/* >          NEGCNT is INTEGER */
/* >           If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin */
/* >           in the  matrix factorization L D L**T, and NEGCNT = -1 otherwise. */
/* > \endverbatim */
/* > */
/* > \param[out] ZTZ */
/* > \verbatim */
/* >          ZTZ is REAL */
/* >           The square of the 2-norm of Z. */
/* > \endverbatim */
/* > */
/* > \param[out] MINGMA */
/* > \verbatim */
/* >          MINGMA is REAL */
/* >           The reciprocal of the largest (in magnitude) diagonal */
/* >           element of the inverse of L D L**T - sigma I. */
/* > \endverbatim */
/* > */
/* > \param[in,out] R */
/* > \verbatim */
/* >          R is INTEGER */
/* >           The twist index for the twisted factorization used to */
/* >           compute Z. */
/* >           On input, 0 <= R <= N. If R is input as 0, R is set to */
/* >           the index where (L D L**T - sigma I)^{-1} is largest */
/* >           in magnitude. If 1 <= R <= N, R is unchanged. */
/* >           On output, R contains the twist index used to compute Z. */
/* >           Ideally, R designates the position of the maximum entry in the */
/* >           eigenvector. */
/* > \endverbatim */
/* > */
/* > \param[out] ISUPPZ */
/* > \verbatim */
/* >          ISUPPZ is INTEGER array, dimension (2) */
/* >           The support of the vector in Z, i.e., the vector Z is */
/* >           nonzero only in elements ISUPPZ(1) through ISUPPZ( 2 ). */
/* > \endverbatim */
/* > */
/* > \param[out] NRMINV */
/* > \verbatim */
/* >          NRMINV is REAL */
/* >           NRMINV = 1/SQRT( ZTZ ) */
/* > \endverbatim */
/* > */
/* > \param[out] RESID */
/* > \verbatim */
/* >          RESID is REAL */
/* >           The residual of the FP vector. */
/* >           RESID = ABS( MINGMA )/SQRT( ZTZ ) */
/* > \endverbatim */
/* > */
/* > \param[out] RQCORR */
/* > \verbatim */
/* >          RQCORR is REAL */
/* >           The Rayleigh Quotient correction to LAMBDA. */
/* >           RQCORR = MINGMA*TMP */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL array, dimension (4*N) */
/* > \endverbatim */

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

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

/* > \date December 2016 */

/* > \ingroup complexOTHERauxiliary */

/* > \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 clar1v_(integer *n, integer *b1, integer *bn, real *
	lambda, real *d__, real *l, real *ld, real *lld, real *pivmin, real *
	gaptol, complex *z__, logical *wantnc, integer *negcnt, real *ztz, 
	real *mingma, integer *r__, integer *isuppz, real *nrminv, real *
	resid, real *rqcorr, real *work)
{
    /* System generated locals */
    integer i__1, i__2, i__3, i__4;
    real r__1;
    complex q__1, q__2;

    /* Local variables */
    integer indp, inds, i__;
    real s, dplus;
    integer r1, r2;
    extern real slamch_(char *);
    integer indlpl, indumn;
    extern logical sisnan_(real *);
    real dminus;
    logical sawnan1, sawnan2;
    real eps, tmp;
    integer neg1, neg2;


/*  -- LAPACK auxiliary routine (version 3.7.0) -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/*     December 2016 */


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


    /* Parameter adjustments */
    --work;
    --isuppz;
    --z__;
    --lld;
    --ld;
    --l;
    --d__;

    /* Function Body */
    eps = slamch_("Precision");
    if (*r__ == 0) {
	r1 = *b1;
	r2 = *bn;
    } else {
	r1 = *r__;
	r2 = *r__;
    }
/*     Storage for LPLUS */
    indlpl = 0;
/*     Storage for UMINUS */
    indumn = *n;
    inds = (*n << 1) + 1;
    indp = *n * 3 + 1;
    if (*b1 == 1) {
	work[inds] = 0.f;
    } else {
	work[inds + *b1 - 1] = lld[*b1 - 1];
    }

/*     Compute the stationary transform (using the differential form) */
/*     until the index R2. */

    sawnan1 = FALSE_;
    neg1 = 0;
    s = work[inds + *b1 - 1] - *lambda;
    i__1 = r1 - 1;
    for (i__ = *b1; i__ <= i__1; ++i__) {
	dplus = d__[i__] + s;
	work[indlpl + i__] = ld[i__] / dplus;
	if (dplus < 0.f) {
	    ++neg1;
	}
	work[inds + i__] = s * work[indlpl + i__] * l[i__];
	s = work[inds + i__] - *lambda;
/* L50: */
    }
    sawnan1 = sisnan_(&s);
    if (sawnan1) {
	goto L60;
    }
    i__1 = r2 - 1;
    for (i__ = r1; i__ <= i__1; ++i__) {
	dplus = d__[i__] + s;
	work[indlpl + i__] = ld[i__] / dplus;
	work[inds + i__] = s * work[indlpl + i__] * l[i__];
	s = work[inds + i__] - *lambda;
/* L51: */
    }
    sawnan1 = sisnan_(&s);

L60:
    if (sawnan1) {
/*        Runs a slower version of the above loop if a NaN is detected */
	neg1 = 0;
	s = work[inds + *b1 - 1] - *lambda;
	i__1 = r1 - 1;
	for (i__ = *b1; i__ <= i__1; ++i__) {
	    dplus = d__[i__] + s;
	    if (abs(dplus) < *pivmin) {
		dplus = -(*pivmin);
	    }
	    work[indlpl + i__] = ld[i__] / dplus;
	    if (dplus < 0.f) {
		++neg1;
	    }
	    work[inds + i__] = s * work[indlpl + i__] * l[i__];
	    if (work[indlpl + i__] == 0.f) {
		work[inds + i__] = lld[i__];
	    }
	    s = work[inds + i__] - *lambda;
/* L70: */
	}
	i__1 = r2 - 1;
	for (i__ = r1; i__ <= i__1; ++i__) {
	    dplus = d__[i__] + s;
	    if (abs(dplus) < *pivmin) {
		dplus = -(*pivmin);
	    }
	    work[indlpl + i__] = ld[i__] / dplus;
	    work[inds + i__] = s * work[indlpl + i__] * l[i__];
	    if (work[indlpl + i__] == 0.f) {
		work[inds + i__] = lld[i__];
	    }
	    s = work[inds + i__] - *lambda;
/* L71: */
	}
    }

/*     Compute the progressive transform (using the differential form) */
/*     until the index R1 */

    sawnan2 = FALSE_;
    neg2 = 0;
    work[indp + *bn - 1] = d__[*bn] - *lambda;
    i__1 = r1;
    for (i__ = *bn - 1; i__ >= i__1; --i__) {
	dminus = lld[i__] + work[indp + i__];
	tmp = d__[i__] / dminus;
	if (dminus < 0.f) {
	    ++neg2;
	}
	work[indumn + i__] = l[i__] * tmp;
	work[indp + i__ - 1] = work[indp + i__] * tmp - *lambda;
/* L80: */
    }
    tmp = work[indp + r1 - 1];
    sawnan2 = sisnan_(&tmp);
    if (sawnan2) {
/*        Runs a slower version of the above loop if a NaN is detected */
	neg2 = 0;
	i__1 = r1;
	for (i__ = *bn - 1; i__ >= i__1; --i__) {
	    dminus = lld[i__] + work[indp + i__];
	    if (abs(dminus) < *pivmin) {
		dminus = -(*pivmin);
	    }
	    tmp = d__[i__] / dminus;
	    if (dminus < 0.f) {
		++neg2;
	    }
	    work[indumn + i__] = l[i__] * tmp;
	    work[indp + i__ - 1] = work[indp + i__] * tmp - *lambda;
	    if (tmp == 0.f) {
		work[indp + i__ - 1] = d__[i__] - *lambda;
	    }
/* L100: */
	}
    }

/*     Find the index (from R1 to R2) of the largest (in magnitude) */
/*     diagonal element of the inverse */

    *mingma = work[inds + r1 - 1] + work[indp + r1 - 1];
    if (*mingma < 0.f) {
	++neg1;
    }
    if (*wantnc) {
	*negcnt = neg1 + neg2;
    } else {
	*negcnt = -1;
    }
    if (abs(*mingma) == 0.f) {
	*mingma = eps * work[inds + r1 - 1];
    }
    *r__ = r1;
    i__1 = r2 - 1;
    for (i__ = r1; i__ <= i__1; ++i__) {
	tmp = work[inds + i__] + work[indp + i__];
	if (tmp == 0.f) {
	    tmp = eps * work[inds + i__];
	}
	if (abs(tmp) <= abs(*mingma)) {
	    *mingma = tmp;
	    *r__ = i__ + 1;
	}
/* L110: */
    }

/*     Compute the FP vector: solve N^T v = e_r */

    isuppz[1] = *b1;
    isuppz[2] = *bn;
    i__1 = *r__;
    z__[i__1].r = 1.f, z__[i__1].i = 0.f;
    *ztz = 1.f;

/*     Compute the FP vector upwards from R */

    if (! sawnan1 && ! sawnan2) {
	i__1 = *b1;
	for (i__ = *r__ - 1; i__ >= i__1; --i__) {
	    i__2 = i__;
	    i__3 = indlpl + i__;
	    i__4 = i__ + 1;
	    q__2.r = work[i__3] * z__[i__4].r, q__2.i = work[i__3] * z__[i__4]
		    .i;
	    q__1.r = -q__2.r, q__1.i = -q__2.i;
	    z__[i__2].r = q__1.r, z__[i__2].i = q__1.i;
	    if ((c_abs(&z__[i__]) + c_abs(&z__[i__ + 1])) * (r__1 = ld[i__], 
		    abs(r__1)) < *gaptol) {
		i__2 = i__;
		z__[i__2].r = 0.f, z__[i__2].i = 0.f;
		isuppz[1] = i__ + 1;
		goto L220;
	    }
	    i__2 = i__;
	    i__3 = i__;
	    q__1.r = z__[i__2].r * z__[i__3].r - z__[i__2].i * z__[i__3].i, 
		    q__1.i = z__[i__2].r * z__[i__3].i + z__[i__2].i * z__[
		    i__3].r;
	    *ztz += q__1.r;
/* L210: */
	}
L220:
	;
    } else {
/*        Run slower loop if NaN occurred. */
	i__1 = *b1;
	for (i__ = *r__ - 1; i__ >= i__1; --i__) {
	    i__2 = i__ + 1;
	    if (z__[i__2].r == 0.f && z__[i__2].i == 0.f) {
		i__2 = i__;
		r__1 = -(ld[i__ + 1] / ld[i__]);
		i__3 = i__ + 2;
		q__1.r = r__1 * z__[i__3].r, q__1.i = r__1 * z__[i__3].i;
		z__[i__2].r = q__1.r, z__[i__2].i = q__1.i;
	    } else {
		i__2 = i__;
		i__3 = indlpl + i__;
		i__4 = i__ + 1;
		q__2.r = work[i__3] * z__[i__4].r, q__2.i = work[i__3] * z__[
			i__4].i;
		q__1.r = -q__2.r, q__1.i = -q__2.i;
		z__[i__2].r = q__1.r, z__[i__2].i = q__1.i;
	    }
	    if ((c_abs(&z__[i__]) + c_abs(&z__[i__ + 1])) * (r__1 = ld[i__], 
		    abs(r__1)) < *gaptol) {
		i__2 = i__;
		z__[i__2].r = 0.f, z__[i__2].i = 0.f;
		isuppz[1] = i__ + 1;
		goto L240;
	    }
	    i__2 = i__;
	    i__3 = i__;
	    q__1.r = z__[i__2].r * z__[i__3].r - z__[i__2].i * z__[i__3].i, 
		    q__1.i = z__[i__2].r * z__[i__3].i + z__[i__2].i * z__[
		    i__3].r;
	    *ztz += q__1.r;
/* L230: */
	}
L240:
	;
    }
/*     Compute the FP vector downwards from R in blocks of size BLKSIZ */
    if (! sawnan1 && ! sawnan2) {
	i__1 = *bn - 1;
	for (i__ = *r__; i__ <= i__1; ++i__) {
	    i__2 = i__ + 1;
	    i__3 = indumn + i__;
	    i__4 = i__;
	    q__2.r = work[i__3] * z__[i__4].r, q__2.i = work[i__3] * z__[i__4]
		    .i;
	    q__1.r = -q__2.r, q__1.i = -q__2.i;
	    z__[i__2].r = q__1.r, z__[i__2].i = q__1.i;
	    if ((c_abs(&z__[i__]) + c_abs(&z__[i__ + 1])) * (r__1 = ld[i__], 
		    abs(r__1)) < *gaptol) {
		i__2 = i__ + 1;
		z__[i__2].r = 0.f, z__[i__2].i = 0.f;
		isuppz[2] = i__;
		goto L260;
	    }
	    i__2 = i__ + 1;
	    i__3 = i__ + 1;
	    q__1.r = z__[i__2].r * z__[i__3].r - z__[i__2].i * z__[i__3].i, 
		    q__1.i = z__[i__2].r * z__[i__3].i + z__[i__2].i * z__[
		    i__3].r;
	    *ztz += q__1.r;
/* L250: */
	}
L260:
	;
    } else {
/*        Run slower loop if NaN occurred. */
	i__1 = *bn - 1;
	for (i__ = *r__; i__ <= i__1; ++i__) {
	    i__2 = i__;
	    if (z__[i__2].r == 0.f && z__[i__2].i == 0.f) {
		i__2 = i__ + 1;
		r__1 = -(ld[i__ - 1] / ld[i__]);
		i__3 = i__ - 1;
		q__1.r = r__1 * z__[i__3].r, q__1.i = r__1 * z__[i__3].i;
		z__[i__2].r = q__1.r, z__[i__2].i = q__1.i;
	    } else {
		i__2 = i__ + 1;
		i__3 = indumn + i__;
		i__4 = i__;
		q__2.r = work[i__3] * z__[i__4].r, q__2.i = work[i__3] * z__[
			i__4].i;
		q__1.r = -q__2.r, q__1.i = -q__2.i;
		z__[i__2].r = q__1.r, z__[i__2].i = q__1.i;
	    }
	    if ((c_abs(&z__[i__]) + c_abs(&z__[i__ + 1])) * (r__1 = ld[i__], 
		    abs(r__1)) < *gaptol) {
		i__2 = i__ + 1;
		z__[i__2].r = 0.f, z__[i__2].i = 0.f;
		isuppz[2] = i__;
		goto L280;
	    }
	    i__2 = i__ + 1;
	    i__3 = i__ + 1;
	    q__1.r = z__[i__2].r * z__[i__3].r - z__[i__2].i * z__[i__3].i, 
		    q__1.i = z__[i__2].r * z__[i__3].i + z__[i__2].i * z__[
		    i__3].r;
	    *ztz += q__1.r;
/* L270: */
	}
L280:
	;
    }

/*     Compute quantities for convergence test */

    tmp = 1.f / *ztz;
    *nrminv = sqrt(tmp);
    *resid = abs(*mingma) * *nrminv;
    *rqcorr = *mingma * tmp;


    return;

/*     End of CLAR1V */

} /* clar1v_ */