OpenBLAS/lapack-netlib/SRC/slarrd.c

/* f2c.h  --  Standard Fortran to C header file */

/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."

	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */

#ifndef F2C_INCLUDE
#define F2C_INCLUDE

#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

typedef int 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;
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;}
#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)); }
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#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) = conj(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) (cimag(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;
}
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;
}
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;
}
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;
	_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;
}
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
	_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;
}	
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
	_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;
}
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
	_Complex double zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cd(&x[i]) * Cd(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
		}
	}
	pCd(z) = zdotc;
}
#endif
/*  -- translated by f2c (version 20000121).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/



/* Table of constant values */

static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
static integer c__0 = 0;

/* > \brief \b SLARRD computes the eigenvalues of a symmetric tridiagonal matrix to suitable accuracy. */

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

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

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

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

/*       SUBROUTINE SLARRD( RANGE, ORDER, N, VL, VU, IL, IU, GERS, */
/*                           RELTOL, D, E, E2, PIVMIN, NSPLIT, ISPLIT, */
/*                           M, W, WERR, WL, WU, IBLOCK, INDEXW, */
/*                           WORK, IWORK, INFO ) */

/*       CHARACTER          ORDER, RANGE */
/*       INTEGER            IL, INFO, IU, M, N, NSPLIT */
/*       REAL                PIVMIN, RELTOL, VL, VU, WL, WU */
/*       INTEGER            IBLOCK( * ), INDEXW( * ), */
/*      $                   ISPLIT( * ), IWORK( * ) */
/*       REAL               D( * ), E( * ), E2( * ), */
/*      $                   GERS( * ), W( * ), WERR( * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SLARRD computes the eigenvalues of a symmetric tridiagonal */
/* > matrix T to suitable accuracy. This is an auxiliary code to be */
/* > called from SSTEMR. */
/* > The user may ask for all eigenvalues, all eigenvalues */
/* > in the half-open interval (VL, VU], or the IL-th through IU-th */
/* > eigenvalues. */
/* > */
/* > To avoid overflow, the matrix must be scaled so that its */
/* > largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
 */
/* > accuracy, it should not be much smaller than that. */
/* > */
/* > See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal */
/* > Matrix", Report CS41, Computer Science Dept., Stanford */
/* > University, July 21, 1966. */
/* > \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] ORDER */
/* > \verbatim */
/* >          ORDER is CHARACTER*1 */
/* >          = 'B': ("By Block") the eigenvalues will be grouped by */
/* >                              split-off block (see IBLOCK, ISPLIT) and */
/* >                              ordered from smallest to largest within */
/* >                              the block. */
/* >          = 'E': ("Entire matrix") */
/* >                              the eigenvalues for the entire matrix */
/* >                              will be ordered from smallest to */
/* >                              largest. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the tridiagonal matrix T.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] VL */
/* > \verbatim */
/* >          VL is REAL */
/* >          If RANGE='V', the lower bound of the interval to */
/* >          be searched for eigenvalues.  Eigenvalues less than or equal */
/* >          to VL, or greater than VU, will not be returned.  VL < VU. */
/* >          Not referenced if RANGE = 'A' or 'I'. */
/* > \endverbatim */
/* > */
/* > \param[in] VU */
/* > \verbatim */
/* >          VU is REAL */
/* >          If RANGE='V', the upper bound of the interval to */
/* >          be searched for eigenvalues.  Eigenvalues less than or equal */
/* >          to VL, or greater than VU, will not be returned.  VL < VU. */
/* >          Not referenced if RANGE = 'A' or 'I'. */
/* > \endverbatim */
/* > */
/* > \param[in] IL */
/* > \verbatim */
/* >          IL is INTEGER */
/* >          If RANGE='I', the index of the */
/* >          smallest eigenvalue to be returned. */
/* >          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
/* >          Not referenced if RANGE = 'A' or 'V'. */
/* > \endverbatim */
/* > */
/* > \param[in] IU */
/* > \verbatim */
/* >          IU is INTEGER */
/* >          If RANGE='I', the index of the */
/* >          largest eigenvalue to be returned. */
/* >          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
/* >          Not referenced if RANGE = 'A' or 'V'. */
/* > \endverbatim */
/* > */
/* > \param[in] GERS */
/* > \verbatim */
/* >          GERS is REAL array, dimension (2*N) */
/* >          The N Gerschgorin intervals (the i-th Gerschgorin interval */
/* >          is (GERS(2*i-1), GERS(2*i)). */
/* > \endverbatim */
/* > */
/* > \param[in] RELTOL */
/* > \verbatim */
/* >          RELTOL is REAL */
/* >          The minimum relative width of an interval.  When an interval */
/* >          is narrower than RELTOL times the larger (in */
/* >          magnitude) endpoint, then it is considered to be */
/* >          sufficiently small, i.e., converged.  Note: this should */
/* >          always be at least radix*machine epsilon. */
/* > \endverbatim */
/* > */
/* > \param[in] D */
/* > \verbatim */
/* >          D is REAL array, dimension (N) */
/* >          The n diagonal elements of the tridiagonal matrix T. */
/* > \endverbatim */
/* > */
/* > \param[in] E */
/* > \verbatim */
/* >          E is REAL array, dimension (N-1) */
/* >          The (n-1) off-diagonal elements of the tridiagonal matrix T. */
/* > \endverbatim */
/* > */
/* > \param[in] E2 */
/* > \verbatim */
/* >          E2 is REAL array, dimension (N-1) */
/* >          The (n-1) squared off-diagonal elements of the tridiagonal matrix T. */
/* > \endverbatim */
/* > */
/* > \param[in] PIVMIN */
/* > \verbatim */
/* >          PIVMIN is REAL */
/* >          The minimum pivot allowed in the Sturm sequence for T. */
/* > \endverbatim */
/* > */
/* > \param[in] NSPLIT */
/* > \verbatim */
/* >          NSPLIT is INTEGER */
/* >          The number of diagonal blocks in the matrix T. */
/* >          1 <= NSPLIT <= N. */
/* > \endverbatim */
/* > */
/* > \param[in] ISPLIT */
/* > \verbatim */
/* >          ISPLIT is INTEGER array, dimension (N) */
/* >          The splitting points, at which T breaks up into submatrices. */
/* >          The first submatrix 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. */
/* >          (Only the first NSPLIT elements will actually be used, but */
/* >          since the user cannot know a priori what value NSPLIT will */
/* >          have, N words must be reserved for ISPLIT.) */
/* > \endverbatim */
/* > */
/* > \param[out] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The actual number of eigenvalues found. 0 <= M <= N. */
/* >          (See also the description of INFO=2,3.) */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* >          W is REAL array, dimension (N) */
/* >          On exit, the first M elements of W will contain the */
/* >          eigenvalue approximations. SLARRD computes an interval */
/* >          I_j = (a_j, b_j] that includes eigenvalue j. The eigenvalue */
/* >          approximation is given as the interval midpoint */
/* >          W(j)= ( a_j + b_j)/2. The corresponding error is bounded by */
/* >          WERR(j) = abs( a_j - b_j)/2 */
/* > \endverbatim */
/* > */
/* > \param[out] WERR */
/* > \verbatim */
/* >          WERR is REAL array, dimension (N) */
/* >          The error bound on the corresponding eigenvalue approximation */
/* >          in W. */
/* > \endverbatim */
/* > */
/* > \param[out] WL */
/* > \verbatim */
/* >          WL is REAL */
/* > \endverbatim */
/* > */
/* > \param[out] WU */
/* > \verbatim */
/* >          WU is REAL */
/* >          The interval (WL, WU] contains all the wanted eigenvalues. */
/* >          If RANGE='V', then WL=VL and WU=VU. */
/* >          If RANGE='A', then WL and WU are the global Gerschgorin bounds */
/* >                        on the spectrum. */
/* >          If RANGE='I', then WL and WU are computed by SLAEBZ from the */
/* >                        index range specified. */
/* > \endverbatim */
/* > */
/* > \param[out] IBLOCK */
/* > \verbatim */
/* >          IBLOCK is INTEGER array, dimension (N) */
/* >          At each row/column j where E(j) is zero or small, the */
/* >          matrix T is considered to split into a block diagonal */
/* >          matrix.  On exit, if INFO = 0, IBLOCK(i) specifies to which */
/* >          block (from 1 to the number of blocks) the eigenvalue W(i) */
/* >          belongs.  (SLARRD may use the remaining N-M elements as */
/* >          workspace.) */
/* > \endverbatim */
/* > */
/* > \param[out] INDEXW */
/* > \verbatim */
/* >          INDEXW is INTEGER array, dimension (N) */
/* >          The indices of the eigenvalues within each block (submatrix); */
/* >          for example, INDEXW(i)= j and IBLOCK(i)=k imply that the */
/* >          i-th eigenvalue W(i) is the j-th eigenvalue in block k. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL array, dimension (4*N) */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (3*N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit */
/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
/* >          > 0:  some or all of the eigenvalues failed to converge or */
/* >                were not computed: */
/* >                =1 or 3: Bisection failed to converge for some */
/* >                        eigenvalues; these eigenvalues are flagged by a */
/* >                        negative block number.  The effect is that the */
/* >                        eigenvalues may not be as accurate as the */
/* >                        absolute and relative tolerances.  This is */
/* >                        generally caused by unexpectedly inaccurate */
/* >                        arithmetic. */
/* >                =2 or 3: RANGE='I' only: Not all of the eigenvalues */
/* >                        IL:IU were found. */
/* >                        Effect: M < IU+1-IL */
/* >                        Cause:  non-monotonic arithmetic, causing the */
/* >                                Sturm sequence to be non-monotonic. */
/* >                        Cure:   recalculate, using RANGE='A', and pick */
/* >                                out eigenvalues IL:IU.  In some cases, */
/* >                                increasing the PARAMETER "FUDGE" may */
/* >                                make things work. */
/* >                = 4:    RANGE='I', and the Gershgorin interval */
/* >                        initially used was too small.  No eigenvalues */
/* >                        were computed. */
/* >                        Probable cause: your machine has sloppy */
/* >                                        floating-point arithmetic. */
/* >                        Cure: Increase the PARAMETER "FUDGE", */
/* >                              recompile, and try again. */
/* > \endverbatim */

/* > \par Internal Parameters: */
/*  ========================= */
/* > */
/* > \verbatim */
/* >  FUDGE   REAL, default = 2 */
/* >          A "fudge factor" to widen the Gershgorin intervals.  Ideally, */
/* >          a value of 1 should work, but on machines with sloppy */
/* >          arithmetic, this needs to be larger.  The default for */
/* >          publicly released versions should be large enough to handle */
/* >          the worst machine around.  Note that this has no effect */
/* >          on accuracy of the solution. */
/* > \endverbatim */
/* > */
/* > \par Contributors: */
/*  ================== */
/* > */
/* >     W. Kahan, University of California, Berkeley, USA \n */
/* >     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 */

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

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

/* > \date June 2016 */

/* > \ingroup OTHERauxiliary */

/*  ===================================================================== */
/* Subroutine */ int slarrd_(char *range, char *order, integer *n, real *vl, 
	real *vu, integer *il, integer *iu, real *gers, real *reltol, real *
	d__, real *e, real *e2, real *pivmin, integer *nsplit, integer *
	isplit, integer *m, real *w, real *werr, real *wl, real *wu, integer *
	iblock, integer *indexw, real *work, integer *iwork, integer *info)
{
    /* System generated locals */
    integer i__1, i__2, i__3;
    real r__1, r__2;

    /* Local variables */
    integer iend, jblk, ioff, iout, itmp1, itmp2, i__, j, jdisc;
    extern logical lsame_(char *, char *);
    integer iinfo;
    real atoli;
    integer iwoff, itmax;
    real wkill, rtoli, uflow, tnorm;
    integer ib, ie, je, nb;
    real gl;
    integer im, in;
    real gu;
    integer ibegin, iw, irange, idiscl;
    extern real slamch_(char *);
    integer idumma[1];
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    integer idiscu;
    extern /* Subroutine */ int slaebz_(integer *, integer *, integer *, 
	    integer *, integer *, integer *, real *, real *, real *, real *, 
	    real *, real *, integer *, real *, real *, integer *, integer *, 
	    real *, integer *, integer *);
    logical ncnvrg, toofew;
    integer jee;
    real eps;
    integer nwl;
    real wlu, wul;
    integer nwu;
    real tmp1, tmp2;


/*  -- LAPACK auxiliary routine (version 3.7.1) -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/*     June 2016 */


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


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

    /* Function Body */
    *info = 0;

/*     Quick return if possible */

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

/*     Decode RANGE */

    if (lsame_(range, "A")) {
	irange = 1;
    } else if (lsame_(range, "V")) {
	irange = 2;
    } else if (lsame_(range, "I")) {
	irange = 3;
    } else {
	irange = 0;
    }

/*     Check for Errors */

    if (irange <= 0) {
	*info = -1;
    } else if (! (lsame_(order, "B") || lsame_(order, 
	    "E"))) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (irange == 2) {
	if (*vl >= *vu) {
	    *info = -5;
	}
    } else if (irange == 3 && (*il < 1 || *il > f2cmax(1,*n))) {
	*info = -6;
    } else if (irange == 3 && (*iu < f2cmin(*n,*il) || *iu > *n)) {
	*info = -7;
    }

    if (*info != 0) {
	return 0;
    }
/*     Initialize error flags */
    *info = 0;
    ncnvrg = FALSE_;
    toofew = FALSE_;
/*     Quick return if possible */
    *m = 0;
    if (*n == 0) {
	return 0;
    }
/*     Simplification: */
    if (irange == 3 && *il == 1 && *iu == *n) {
	irange = 1;
    }
/*     Get machine constants */
    eps = slamch_("P");
    uflow = slamch_("U");
/*     Special Case when N=1 */
/*     Treat case of 1x1 matrix for quick return */
    if (*n == 1) {
	if (irange == 1 || irange == 2 && d__[1] > *vl && d__[1] <= *vu || 
		irange == 3 && *il == 1 && *iu == 1) {
	    *m = 1;
	    w[1] = d__[1];
/*           The computation error of the eigenvalue is zero */
	    werr[1] = 0.f;
	    iblock[1] = 1;
	    indexw[1] = 1;
	}
	return 0;
    }
/*     NB is the minimum vector length for vector bisection, or 0 */
/*     if only scalar is to be done. */
    nb = ilaenv_(&c__1, "SSTEBZ", " ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
	    ftnlen)1);
    if (nb <= 1) {
	nb = 0;
    }
/*     Find global spectral radius */
    gl = d__[1];
    gu = d__[1];
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MIN */
	r__1 = gl, r__2 = gers[(i__ << 1) - 1];
	gl = f2cmin(r__1,r__2);
/* Computing MAX */
	r__1 = gu, r__2 = gers[i__ * 2];
	gu = f2cmax(r__1,r__2);
/* L5: */
    }
/*     Compute global Gerschgorin bounds and spectral diameter */
/* Computing MAX */
    r__1 = abs(gl), r__2 = abs(gu);
    tnorm = f2cmax(r__1,r__2);
    gl = gl - tnorm * 2.f * eps * *n - *pivmin * 4.f;
    gu = gu + tnorm * 2.f * eps * *n + *pivmin * 4.f;
/*     [JAN/28/2009] remove the line below since SPDIAM variable not use */
/*     SPDIAM = GU - GL */
/*     Input arguments for SLAEBZ: */
/*     The relative tolerance.  An interval (a,b] lies within */
/*     "relative tolerance" if  b-a < RELTOL*f2cmax(|a|,|b|), */
    rtoli = *reltol;
/*     Set the absolute tolerance for interval convergence to zero to force */
/*     interval convergence based on relative size of the interval. */
/*     This is dangerous because intervals might not converge when RELTOL is */
/*     small. But at least a very small number should be selected so that for */
/*     strongly graded matrices, the code can get relatively accurate */
/*     eigenvalues. */
    atoli = uflow * 4.f + *pivmin * 4.f;
    if (irange == 3) {
/*        RANGE='I': Compute an interval containing eigenvalues */
/*        IL through IU. The initial interval [GL,GU] from the global */
/*        Gerschgorin bounds GL and GU is refined by SLAEBZ. */
	itmax = (integer) ((log(tnorm + *pivmin) - log(*pivmin)) / log(2.f)) 
		+ 2;
	work[*n + 1] = gl;
	work[*n + 2] = gl;
	work[*n + 3] = gu;
	work[*n + 4] = gu;
	work[*n + 5] = gl;
	work[*n + 6] = gu;
	iwork[1] = -1;
	iwork[2] = -1;
	iwork[3] = *n + 1;
	iwork[4] = *n + 1;
	iwork[5] = *il - 1;
	iwork[6] = *iu;

	slaebz_(&c__3, &itmax, n, &c__2, &c__2, &nb, &atoli, &rtoli, pivmin, &
		d__[1], &e[1], &e2[1], &iwork[5], &work[*n + 1], &work[*n + 5]
		, &iout, &iwork[1], &w[1], &iblock[1], &iinfo);
	if (iinfo != 0) {
	    *info = iinfo;
	    return 0;
	}
/*        On exit, output intervals may not be ordered by ascending negcount */
	if (iwork[6] == *iu) {
	    *wl = work[*n + 1];
	    wlu = work[*n + 3];
	    nwl = iwork[1];
	    *wu = work[*n + 4];
	    wul = work[*n + 2];
	    nwu = iwork[4];
	} else {
	    *wl = work[*n + 2];
	    wlu = work[*n + 4];
	    nwl = iwork[2];
	    *wu = work[*n + 3];
	    wul = work[*n + 1];
	    nwu = iwork[3];
	}
/*        On exit, the interval [WL, WLU] contains a value with negcount NWL, */
/*        and [WUL, WU] contains a value with negcount NWU. */
	if (nwl < 0 || nwl >= *n || nwu < 1 || nwu > *n) {
	    *info = 4;
	    return 0;
	}
    } else if (irange == 2) {
	*wl = *vl;
	*wu = *vu;
    } else if (irange == 1) {
	*wl = gl;
	*wu = gu;
    }
/*     Find Eigenvalues -- Loop Over blocks and recompute NWL and NWU. */
/*     NWL accumulates the number of eigenvalues .le. WL, */
/*     NWU accumulates the number of eigenvalues .le. WU */
    *m = 0;
    iend = 0;
    *info = 0;
    nwl = 0;
    nwu = 0;

    i__1 = *nsplit;
    for (jblk = 1; jblk <= i__1; ++jblk) {
	ioff = iend;
	ibegin = ioff + 1;
	iend = isplit[jblk];
	in = iend - ioff;

	if (in == 1) {
/*           1x1 block */
	    if (*wl >= d__[ibegin] - *pivmin) {
		++nwl;
	    }
	    if (*wu >= d__[ibegin] - *pivmin) {
		++nwu;
	    }
	    if (irange == 1 || *wl < d__[ibegin] - *pivmin && *wu >= d__[
		    ibegin] - *pivmin) {
		++(*m);
		w[*m] = d__[ibegin];
		werr[*m] = 0.f;
/*              The gap for a single block doesn't matter for the later */
/*              algorithm and is assigned an arbitrary large value */
		iblock[*m] = jblk;
		indexw[*m] = 1;
	    }
/*        Disabled 2x2 case because of a failure on the following matrix */
/*        RANGE = 'I', IL = IU = 4 */
/*          Original Tridiagonal, d = [ */
/*           -0.150102010615740E+00 */
/*           -0.849897989384260E+00 */
/*           -0.128208148052635E-15 */
/*            0.128257718286320E-15 */
/*          ]; */
/*          e = [ */
/*           -0.357171383266986E+00 */
/*           -0.180411241501588E-15 */
/*           -0.175152352710251E-15 */
/*          ]; */

/*         ELSE IF( IN.EQ.2 ) THEN */
/* *           2x2 block */
/*            DISC = SQRT( (HALF*(D(IBEGIN)-D(IEND)))**2 + E(IBEGIN)**2 ) */
/*            TMP1 = HALF*(D(IBEGIN)+D(IEND)) */
/*            L1 = TMP1 - DISC */
/*            IF( WL.GE. L1-PIVMIN ) */
/*     $         NWL = NWL + 1 */
/*            IF( WU.GE. L1-PIVMIN ) */
/*     $         NWU = NWU + 1 */
/*            IF( IRANGE.EQ.ALLRNG .OR. ( WL.LT.L1-PIVMIN .AND. WU.GE. */
/*     $          L1-PIVMIN ) ) THEN */
/*               M = M + 1 */
/*               W( M ) = L1 */
/* *              The uncertainty of eigenvalues of a 2x2 matrix is very small */
/*               WERR( M ) = EPS * ABS( W( M ) ) * TWO */
/*               IBLOCK( M ) = JBLK */
/*               INDEXW( M ) = 1 */
/*            ENDIF */
/*            L2 = TMP1 + DISC */
/*            IF( WL.GE. L2-PIVMIN ) */
/*     $         NWL = NWL + 1 */
/*            IF( WU.GE. L2-PIVMIN ) */
/*     $         NWU = NWU + 1 */
/*            IF( IRANGE.EQ.ALLRNG .OR. ( WL.LT.L2-PIVMIN .AND. WU.GE. */
/*     $          L2-PIVMIN ) ) THEN */
/*               M = M + 1 */
/*               W( M ) = L2 */
/* *              The uncertainty of eigenvalues of a 2x2 matrix is very small */
/*               WERR( M ) = EPS * ABS( W( M ) ) * TWO */
/*               IBLOCK( M ) = JBLK */
/*               INDEXW( M ) = 2 */
/*            ENDIF */
	} else {
/*           General Case - block of size IN >= 2 */
/*           Compute local Gerschgorin interval and use it as the initial */
/*           interval for SLAEBZ */
	    gu = d__[ibegin];
	    gl = d__[ibegin];
	    tmp1 = 0.f;
	    i__2 = iend;
	    for (j = ibegin; j <= i__2; ++j) {
/* Computing MIN */
		r__1 = gl, r__2 = gers[(j << 1) - 1];
		gl = f2cmin(r__1,r__2);
/* Computing MAX */
		r__1 = gu, r__2 = gers[j * 2];
		gu = f2cmax(r__1,r__2);
/* L40: */
	    }
/*           [JAN/28/2009] */
/*           change SPDIAM by TNORM in lines 2 and 3 thereafter */
/*           line 1: remove computation of SPDIAM (not useful anymore) */
/*           SPDIAM = GU - GL */
/*           GL = GL - FUDGE*SPDIAM*EPS*IN - FUDGE*PIVMIN */
/*           GU = GU + FUDGE*SPDIAM*EPS*IN + FUDGE*PIVMIN */
	    gl = gl - tnorm * 2.f * eps * in - *pivmin * 2.f;
	    gu = gu + tnorm * 2.f * eps * in + *pivmin * 2.f;

	    if (irange > 1) {
		if (gu < *wl) {
/*                 the local block contains none of the wanted eigenvalues */
		    nwl += in;
		    nwu += in;
		    goto L70;
		}
/*              refine search interval if possible, only range (WL,WU] matters */
		gl = f2cmax(gl,*wl);
		gu = f2cmin(gu,*wu);
		if (gl >= gu) {
		    goto L70;
		}
	    }
/*           Find negcount of initial interval boundaries GL and GU */
	    work[*n + 1] = gl;
	    work[*n + in + 1] = gu;
	    slaebz_(&c__1, &c__0, &in, &in, &c__1, &nb, &atoli, &rtoli, 
		    pivmin, &d__[ibegin], &e[ibegin], &e2[ibegin], idumma, &
		    work[*n + 1], &work[*n + (in << 1) + 1], &im, &iwork[1], &
		    w[*m + 1], &iblock[*m + 1], &iinfo);
	    if (iinfo != 0) {
		*info = iinfo;
		return 0;
	    }

	    nwl += iwork[1];
	    nwu += iwork[in + 1];
	    iwoff = *m - iwork[1];
/*           Compute Eigenvalues */
	    itmax = (integer) ((log(gu - gl + *pivmin) - log(*pivmin)) / log(
		    2.f)) + 2;
	    slaebz_(&c__2, &itmax, &in, &in, &c__1, &nb, &atoli, &rtoli, 
		    pivmin, &d__[ibegin], &e[ibegin], &e2[ibegin], idumma, &
		    work[*n + 1], &work[*n + (in << 1) + 1], &iout, &iwork[1],
		     &w[*m + 1], &iblock[*m + 1], &iinfo);
	    if (iinfo != 0) {
		*info = iinfo;
		return 0;
	    }

/*           Copy eigenvalues into W and IBLOCK */
/*           Use -JBLK for block number for unconverged eigenvalues. */
/*           Loop over the number of output intervals from SLAEBZ */
	    i__2 = iout;
	    for (j = 1; j <= i__2; ++j) {
/*              eigenvalue approximation is middle point of interval */
		tmp1 = (work[j + *n] + work[j + in + *n]) * .5f;
/*              semi length of error interval */
		tmp2 = (r__1 = work[j + *n] - work[j + in + *n], abs(r__1)) * 
			.5f;
		if (j > iout - iinfo) {
/*                 Flag non-convergence. */
		    ncnvrg = TRUE_;
		    ib = -jblk;
		} else {
		    ib = jblk;
		}
		i__3 = iwork[j + in] + iwoff;
		for (je = iwork[j] + 1 + iwoff; je <= i__3; ++je) {
		    w[je] = tmp1;
		    werr[je] = tmp2;
		    indexw[je] = je - iwoff;
		    iblock[je] = ib;
/* L50: */
		}
/* L60: */
	    }

	    *m += im;
	}
L70:
	;
    }
/*     If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU */
/*     If NWL+1 < IL or NWU > IU, discard extra eigenvalues. */
    if (irange == 3) {
	idiscl = *il - 1 - nwl;
	idiscu = nwu - *iu;

	if (idiscl > 0) {
	    im = 0;
	    i__1 = *m;
	    for (je = 1; je <= i__1; ++je) {
/*              Remove some of the smallest eigenvalues from the left so that */
/*              at the end IDISCL =0. Move all eigenvalues up to the left. */
		if (w[je] <= wlu && idiscl > 0) {
		    --idiscl;
		} else {
		    ++im;
		    w[im] = w[je];
		    werr[im] = werr[je];
		    indexw[im] = indexw[je];
		    iblock[im] = iblock[je];
		}
/* L80: */
	    }
	    *m = im;
	}
	if (idiscu > 0) {
/*           Remove some of the largest eigenvalues from the right so that */
/*           at the end IDISCU =0. Move all eigenvalues up to the left. */
	    im = *m + 1;
	    for (je = *m; je >= 1; --je) {
		if (w[je] >= wul && idiscu > 0) {
		    --idiscu;
		} else {
		    --im;
		    w[im] = w[je];
		    werr[im] = werr[je];
		    indexw[im] = indexw[je];
		    iblock[im] = iblock[je];
		}
/* L81: */
	    }
	    jee = 0;
	    i__1 = *m;
	    for (je = im; je <= i__1; ++je) {
		++jee;
		w[jee] = w[je];
		werr[jee] = werr[je];
		indexw[jee] = indexw[je];
		iblock[jee] = iblock[je];
/* L82: */
	    }
	    *m = *m - im + 1;
	}
	if (idiscl > 0 || idiscu > 0) {
/*           Code to deal with effects of bad arithmetic. (If N(w) is */
/*           monotone non-decreasing, this should never happen.) */
/*           Some low eigenvalues to be discarded are not in (WL,WLU], */
/*           or high eigenvalues to be discarded are not in (WUL,WU] */
/*           so just kill off the smallest IDISCL/largest IDISCU */
/*           eigenvalues, by marking the corresponding IBLOCK = 0 */
	    if (idiscl > 0) {
		wkill = *wu;
		i__1 = idiscl;
		for (jdisc = 1; jdisc <= i__1; ++jdisc) {
		    iw = 0;
		    i__2 = *m;
		    for (je = 1; je <= i__2; ++je) {
			if (iblock[je] != 0 && (w[je] < wkill || iw == 0)) {
			    iw = je;
			    wkill = w[je];
			}
/* L90: */
		    }
		    iblock[iw] = 0;
/* L100: */
		}
	    }
	    if (idiscu > 0) {
		wkill = *wl;
		i__1 = idiscu;
		for (jdisc = 1; jdisc <= i__1; ++jdisc) {
		    iw = 0;
		    i__2 = *m;
		    for (je = 1; je <= i__2; ++je) {
			if (iblock[je] != 0 && (w[je] >= wkill || iw == 0)) {
			    iw = je;
			    wkill = w[je];
			}
/* L110: */
		    }
		    iblock[iw] = 0;
/* L120: */
		}
	    }
/*           Now erase all eigenvalues with IBLOCK set to zero */
	    im = 0;
	    i__1 = *m;
	    for (je = 1; je <= i__1; ++je) {
		if (iblock[je] != 0) {
		    ++im;
		    w[im] = w[je];
		    werr[im] = werr[je];
		    indexw[im] = indexw[je];
		    iblock[im] = iblock[je];
		}
/* L130: */
	    }
	    *m = im;
	}
	if (idiscl < 0 || idiscu < 0) {
	    toofew = TRUE_;
	}
    }

    if (irange == 1 && *m != *n || irange == 3 && *m != *iu - *il + 1) {
	toofew = TRUE_;
    }
/*     If ORDER='B', do nothing the eigenvalues are already sorted by */
/*        block. */
/*     If ORDER='E', sort the eigenvalues from smallest to largest */
    if (lsame_(order, "E") && *nsplit > 1) {
	i__1 = *m - 1;
	for (je = 1; je <= i__1; ++je) {
	    ie = 0;
	    tmp1 = w[je];
	    i__2 = *m;
	    for (j = je + 1; j <= i__2; ++j) {
		if (w[j] < tmp1) {
		    ie = j;
		    tmp1 = w[j];
		}
/* L140: */
	    }
	    if (ie != 0) {
		tmp2 = werr[ie];
		itmp1 = iblock[ie];
		itmp2 = indexw[ie];
		w[ie] = w[je];
		werr[ie] = werr[je];
		iblock[ie] = iblock[je];
		indexw[ie] = indexw[je];
		w[je] = tmp1;
		werr[je] = tmp2;
		iblock[je] = itmp1;
		indexw[je] = itmp2;
	    }
/* L150: */
	}
    }

    *info = 0;
    if (ncnvrg) {
	++(*info);
    }
    if (toofew) {
	*info += 2;
    }
    return 0;

/*     End of SLARRD */

} /* slarrd_ */