OpenBLAS/lapack-netlib/SRC/sstedc.c

#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif

#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif

#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif

typedef blasint integer;

typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef int logical;
typedef short int shortlogical;
typedef char logical1;
typedef char integer1;

#define TRUE_ (1)
#define FALSE_ (0)

/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif

/* I/O stuff */

typedef int flag;
typedef int ftnlen;
typedef int ftnint;

/*external read, write*/
typedef struct
{	flag cierr;
	ftnint ciunit;
	flag ciend;
	char *cifmt;
	ftnint cirec;
} cilist;

/*internal read, write*/
typedef struct
{	flag icierr;
	char *iciunit;
	flag iciend;
	char *icifmt;
	ftnint icirlen;
	ftnint icirnum;
} icilist;

/*open*/
typedef struct
{	flag oerr;
	ftnint ounit;
	char *ofnm;
	ftnlen ofnmlen;
	char *osta;
	char *oacc;
	char *ofm;
	ftnint orl;
	char *oblnk;
} olist;

/*close*/
typedef struct
{	flag cerr;
	ftnint cunit;
	char *csta;
} cllist;

/*rewind, backspace, endfile*/
typedef struct
{	flag aerr;
	ftnint aunit;
} alist;

/* inquire */
typedef struct
{	flag inerr;
	ftnint inunit;
	char *infile;
	ftnlen infilen;
	ftnint	*inex;	/*parameters in standard's order*/
	ftnint	*inopen;
	ftnint	*innum;
	ftnint	*innamed;
	char	*inname;
	ftnlen	innamlen;
	char	*inacc;
	ftnlen	inacclen;
	char	*inseq;
	ftnlen	inseqlen;
	char 	*indir;
	ftnlen	indirlen;
	char	*infmt;
	ftnlen	infmtlen;
	char	*inform;
	ftnint	informlen;
	char	*inunf;
	ftnlen	inunflen;
	ftnint	*inrecl;
	ftnint	*innrec;
	char	*inblank;
	ftnlen	inblanklen;
} inlist;

#define VOID void

union Multitype {	/* for multiple entry points */
	integer1 g;
	shortint h;
	integer i;
	/* longint j; */
	real r;
	doublereal d;
	complex c;
	doublecomplex z;
	};

typedef union Multitype Multitype;

struct Vardesc {	/* for Namelist */
	char *name;
	char *addr;
	ftnlen *dims;
	int  type;
	};
typedef struct Vardesc Vardesc;

struct Namelist {
	char *name;
	Vardesc **vars;
	int nvars;
	};
typedef struct Namelist Namelist;

#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b)	((a) >> (b) & 1)
#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))

#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}

/* procedure parameter types for -A and -C++ */

#define F2C_proc_par_types 1
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif

static float spow_ui(float x, integer n) {
	float pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
static double dpow_ui(double x, integer n) {
	double pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
#ifdef _MSC_VER
static _Fcomplex cpow_ui(complex x, integer n) {
	complex pow={1.0,0.0}; unsigned long int u;
		if(n != 0) {
		if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
		for(u = n; ; ) {
			if(u & 01) pow.r *= x.r, pow.i *= x.i;
			if(u >>= 1) x.r *= x.r, x.i *= x.i;
			else break;
		}
	}
	_Fcomplex p={pow.r, pow.i};
	return p;
}
#else
static _Complex float cpow_ui(_Complex float x, integer n) {
	_Complex float pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
#endif
#ifdef _MSC_VER
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
	_Dcomplex pow={1.0,0.0}; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
		for(u = n; ; ) {
			if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
			if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
			else break;
		}
	}
	_Dcomplex p = {pow._Val[0], pow._Val[1]};
	return p;
}
#else
static _Complex double zpow_ui(_Complex double x, integer n) {
	_Complex double pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
#endif
static integer pow_ii(integer x, integer n) {
	integer pow; unsigned long int u;
	if (n <= 0) {
		if (n == 0 || x == 1) pow = 1;
		else if (x != -1) pow = x == 0 ? 1/x : 0;
		else n = -n;
	}
	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
		u = n;
		for(pow = 1; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
	double m; integer i, mi;
	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
		if (w[i-1]>m) mi=i ,m=w[i-1];
	return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
	float m; integer i, mi;
	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
		if (w[i-1]>m) mi=i ,m=w[i-1];
	return mi-s+1;
}
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
	_Fcomplex zdotc = {0.0, 0.0};
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
			zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
			zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
		}
	}
	pCf(z) = zdotc;
}
#else
	_Complex float zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
		}
	}
	pCf(z) = zdotc;
}
#endif
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
	_Dcomplex zdotc = {0.0, 0.0};
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
			zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
			zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
		}
	}
	pCd(z) = zdotc;
}
#else
	_Complex double zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
		}
	}
	pCd(z) = zdotc;
}
#endif	
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
	_Fcomplex zdotc = {0.0, 0.0};
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
			zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
			zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
		}
	}
	pCf(z) = zdotc;
}
#else
	_Complex float zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cf(&x[i]) * Cf(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
		}
	}
	pCf(z) = zdotc;
}
#endif
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
	_Dcomplex zdotc = {0.0, 0.0};
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
			zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
			zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
		}
	}
	pCd(z) = zdotc;
}
#else
	_Complex double zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cd(&x[i]) * Cd(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
		}
	}
	pCd(z) = zdotc;
}
#endif
/*  -- translated by f2c (version 20000121).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/




/* Table of constant values */

static integer c__9 = 9;
static integer c__0 = 0;
static integer c__2 = 2;
static real c_b17 = 0.f;
static real c_b18 = 1.f;
static integer c__1 = 1;

/* > \brief \b SSTEDC */

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

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

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

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

/*       SUBROUTINE SSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, */
/*                          LIWORK, INFO ) */

/*       CHARACTER          COMPZ */
/*       INTEGER            INFO, LDZ, LIWORK, LWORK, N */
/*       INTEGER            IWORK( * ) */
/*       REAL               D( * ), E( * ), WORK( * ), Z( LDZ, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SSTEDC computes all eigenvalues and, optionally, eigenvectors of a */
/* > symmetric tridiagonal matrix using the divide and conquer method. */
/* > The eigenvectors of a full or band real symmetric matrix can also be */
/* > found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this */
/* > matrix to tridiagonal form. */
/* > */
/* > This code makes very mild assumptions about floating point */
/* > arithmetic. It will work on machines with a guard digit in */
/* > add/subtract, or on those binary machines without guard digits */
/* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
/* > It could conceivably fail on hexadecimal or decimal machines */
/* > without guard digits, but we know of none.  See SLAED3 for details. */
/* > \endverbatim */

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

/* > \param[in] COMPZ */
/* > \verbatim */
/* >          COMPZ is CHARACTER*1 */
/* >          = 'N':  Compute eigenvalues only. */
/* >          = 'I':  Compute eigenvectors of tridiagonal matrix also. */
/* >          = 'V':  Compute eigenvectors of original dense symmetric */
/* >                  matrix also.  On entry, Z contains the orthogonal */
/* >                  matrix used to reduce the original matrix to */
/* >                  tridiagonal form. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The dimension of the symmetric tridiagonal matrix.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* >          D is REAL array, dimension (N) */
/* >          On entry, the diagonal elements of the tridiagonal matrix. */
/* >          On exit, if INFO = 0, the eigenvalues in ascending order. */
/* > \endverbatim */
/* > */
/* > \param[in,out] E */
/* > \verbatim */
/* >          E is REAL array, dimension (N-1) */
/* >          On entry, the subdiagonal elements of the tridiagonal matrix. */
/* >          On exit, E has been destroyed. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Z */
/* > \verbatim */
/* >          Z is REAL array, dimension (LDZ,N) */
/* >          On entry, if COMPZ = 'V', then Z contains the orthogonal */
/* >          matrix used in the reduction to tridiagonal form. */
/* >          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */
/* >          orthonormal eigenvectors of the original symmetric matrix, */
/* >          and if COMPZ = 'I', Z contains the orthonormal eigenvectors */
/* >          of the symmetric tridiagonal matrix. */
/* >          If  COMPZ = 'N', then Z is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDZ */
/* > \verbatim */
/* >          LDZ is INTEGER */
/* >          The leading dimension of the array Z.  LDZ >= 1. */
/* >          If eigenvectors are desired, then LDZ >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL array, dimension (MAX(1,LWORK)) */
/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* >          LWORK is INTEGER */
/* >          The dimension of the array WORK. */
/* >          If COMPZ = 'N' or N <= 1 then LWORK must be at least 1. */
/* >          If COMPZ = 'V' and N > 1 then LWORK must be at least */
/* >                         ( 1 + 3*N + 2*N*lg N + 4*N**2 ), */
/* >                         where lg( N ) = smallest integer k such */
/* >                         that 2**k >= N. */
/* >          If COMPZ = 'I' and N > 1 then LWORK must be at least */
/* >                         ( 1 + 4*N + N**2 ). */
/* >          Note that for COMPZ = 'I' or 'V', then if N is less than or */
/* >          equal to the minimum divide size, usually 25, then LWORK need */
/* >          only be f2cmax(1,2*(N-1)). */
/* > */
/* >          If LWORK = -1, then a workspace query is assumed; the routine */
/* >          only calculates the optimal size of the WORK array, returns */
/* >          this value as the first entry of the WORK array, and no error */
/* >          message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */
/* >          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LIWORK */
/* > \verbatim */
/* >          LIWORK is INTEGER */
/* >          The dimension of the array IWORK. */
/* >          If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1. */
/* >          If COMPZ = 'V' and N > 1 then LIWORK must be at least */
/* >                         ( 6 + 6*N + 5*N*lg N ). */
/* >          If COMPZ = 'I' and N > 1 then LIWORK must be at least */
/* >                         ( 3 + 5*N ). */
/* >          Note that for COMPZ = 'I' or 'V', then if N is less than or */
/* >          equal to the minimum divide size, usually 25, then LIWORK */
/* >          need only be 1. */
/* > */
/* >          If LIWORK = -1, then a workspace query is assumed; the */
/* >          routine only calculates the optimal size of the IWORK array, */
/* >          returns this value as the first entry of the IWORK array, and */
/* >          no error message related to LIWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit. */
/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
/* >          > 0:  The algorithm failed to compute an eigenvalue while */
/* >                working on the submatrix lying in rows and columns */
/* >                INFO/(N+1) through mod(INFO,N+1). */
/* > \endverbatim */

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

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

/* > \date December 2016 */

/* > \ingroup auxOTHERcomputational */

/* > \par Contributors: */
/*  ================== */
/* > */
/* > Jeff Rutter, Computer Science Division, University of California */
/* > at Berkeley, USA \n */
/* >  Modified by Francoise Tisseur, University of Tennessee */
/* > */
/*  ===================================================================== */
/* Subroutine */ int sstedc_(char *compz, integer *n, real *d__, real *e, 
	real *z__, integer *ldz, real *work, integer *lwork, integer *iwork, 
	integer *liwork, integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1, i__2;
    real r__1, r__2;

    /* Local variables */
    real tiny;
    integer i__, j, k, m;
    real p;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    integer lwmin, start;
    extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *, 
	    integer *), slaed0_(integer *, integer *, integer *, real *, real 
	    *, real *, integer *, real *, integer *, real *, integer *, 
	    integer *);
    integer ii;
    extern real slamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    integer finish;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, 
	    real *, integer *), slaset_(char *, integer *, integer *, 
	    real *, real *, real *, integer *);
    integer liwmin, icompz;
    real orgnrm;
    extern real slanst_(char *, integer *, real *, real *);
    extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *),
	     slasrt_(char *, integer *, real *, integer *);
    logical lquery;
    integer smlsiz;
    extern /* Subroutine */ int ssteqr_(char *, integer *, real *, real *, 
	    real *, integer *, real *, integer *);
    integer storez, strtrw, lgn;
    real eps;


/*  -- LAPACK computational 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 */


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


/*     Test the input parameters. */

    /* Parameter adjustments */
    --d__;
    --e;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;
    lquery = *lwork == -1 || *liwork == -1;

    if (lsame_(compz, "N")) {
	icompz = 0;
    } else if (lsame_(compz, "V")) {
	icompz = 1;
    } else if (lsame_(compz, "I")) {
	icompz = 2;
    } else {
	icompz = -1;
    }
    if (icompz < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*ldz < 1 || icompz > 0 && *ldz < f2cmax(1,*n)) {
	*info = -6;
    }

    if (*info == 0) {

/*        Compute the workspace requirements */

	smlsiz = ilaenv_(&c__9, "SSTEDC", " ", &c__0, &c__0, &c__0, &c__0, (
		ftnlen)6, (ftnlen)1);
	if (*n <= 1 || icompz == 0) {
	    liwmin = 1;
	    lwmin = 1;
	} else if (*n <= smlsiz) {
	    liwmin = 1;
	    lwmin = *n - 1 << 1;
	} else {
	    lgn = (integer) (log((real) (*n)) / log(2.f));
	    if (pow_ii(c__2, lgn) < *n) {
		++lgn;
	    }
	    if (pow_ii(c__2, lgn) < *n) {
		++lgn;
	    }
	    if (icompz == 1) {
/* Computing 2nd power */
		i__1 = *n;
		lwmin = *n * 3 + 1 + (*n << 1) * lgn + (i__1 * i__1 << 2);
		liwmin = *n * 6 + 6 + *n * 5 * lgn;
	    } else if (icompz == 2) {
/* Computing 2nd power */
		i__1 = *n;
		lwmin = (*n << 2) + 1 + i__1 * i__1;
		liwmin = *n * 5 + 3;
	    }
	}
	work[1] = (real) lwmin;
	iwork[1] = liwmin;

	if (*lwork < lwmin && ! lquery) {
	    *info = -8;
	} else if (*liwork < liwmin && ! lquery) {
	    *info = -10;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SSTEDC", &i__1, (ftnlen)6);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	return 0;
    }
    if (*n == 1) {
	if (icompz != 0) {
	    z__[z_dim1 + 1] = 1.f;
	}
	return 0;
    }

/*     If the following conditional clause is removed, then the routine */
/*     will use the Divide and Conquer routine to compute only the */
/*     eigenvalues, which requires (3N + 3N**2) real workspace and */
/*     (2 + 5N + 2N lg(N)) integer workspace. */
/*     Since on many architectures SSTERF is much faster than any other */
/*     algorithm for finding eigenvalues only, it is used here */
/*     as the default. If the conditional clause is removed, then */
/*     information on the size of workspace needs to be changed. */

/*     If COMPZ = 'N', use SSTERF to compute the eigenvalues. */

    if (icompz == 0) {
	ssterf_(n, &d__[1], &e[1], info);
	goto L50;
    }

/*     If N is smaller than the minimum divide size (SMLSIZ+1), then */
/*     solve the problem with another solver. */

    if (*n <= smlsiz) {

	ssteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &work[1], info);

    } else {

/*        If COMPZ = 'V', the Z matrix must be stored elsewhere for later */
/*        use. */

	if (icompz == 1) {
	    storez = *n * *n + 1;
	} else {
	    storez = 1;
	}

	if (icompz == 2) {
	    slaset_("Full", n, n, &c_b17, &c_b18, &z__[z_offset], ldz);
	}

/*        Scale. */

	orgnrm = slanst_("M", n, &d__[1], &e[1]);
	if (orgnrm == 0.f) {
	    goto L50;
	}

	eps = slamch_("Epsilon");

	start = 1;

/*        while ( START <= N ) */

L10:
	if (start <= *n) {

/*           Let FINISH be the position of the next subdiagonal entry */
/*           such that E( FINISH ) <= TINY or FINISH = N if no such */
/*           subdiagonal exists.  The matrix identified by the elements */
/*           between START and FINISH constitutes an independent */
/*           sub-problem. */

	    finish = start;
L20:
	    if (finish < *n) {
		tiny = eps * sqrt((r__1 = d__[finish], abs(r__1))) * sqrt((
			r__2 = d__[finish + 1], abs(r__2)));
		if ((r__1 = e[finish], abs(r__1)) > tiny) {
		    ++finish;
		    goto L20;
		}
	    }

/*           (Sub) Problem determined.  Compute its size and solve it. */

	    m = finish - start + 1;
	    if (m == 1) {
		start = finish + 1;
		goto L10;
	    }
	    if (m > smlsiz) {

/*              Scale. */

		orgnrm = slanst_("M", &m, &d__[start], &e[start]);
		slascl_("G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[
			start], &m, info);
		i__1 = m - 1;
		i__2 = m - 1;
		slascl_("G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[
			start], &i__2, info);

		if (icompz == 1) {
		    strtrw = 1;
		} else {
		    strtrw = start;
		}
		slaed0_(&icompz, n, &m, &d__[start], &e[start], &z__[strtrw + 
			start * z_dim1], ldz, &work[1], n, &work[storez], &
			iwork[1], info);
		if (*info != 0) {
		    *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info %
			     (m + 1) + start - 1;
		    goto L50;
		}

/*              Scale back. */

		slascl_("G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[
			start], &m, info);

	    } else {
		if (icompz == 1) {

/*                 Since QR won't update a Z matrix which is larger than */
/*                 the length of D, we must solve the sub-problem in a */
/*                 workspace and then multiply back into Z. */

		    ssteqr_("I", &m, &d__[start], &e[start], &work[1], &m, &
			    work[m * m + 1], info);
		    slacpy_("A", n, &m, &z__[start * z_dim1 + 1], ldz, &work[
			    storez], n);
		    sgemm_("N", "N", n, &m, &m, &c_b18, &work[storez], n, &
			    work[1], &m, &c_b17, &z__[start * z_dim1 + 1], 
			    ldz);
		} else if (icompz == 2) {
		    ssteqr_("I", &m, &d__[start], &e[start], &z__[start + 
			    start * z_dim1], ldz, &work[1], info);
		} else {
		    ssterf_(&m, &d__[start], &e[start], info);
		}
		if (*info != 0) {
		    *info = start * (*n + 1) + finish;
		    goto L50;
		}
	    }

	    start = finish + 1;
	    goto L10;
	}

/*        endwhile */

	if (icompz == 0) {

/*          Use Quick Sort */

	    slasrt_("I", n, &d__[1], info);

	} else {

/*          Use Selection Sort to minimize swaps of eigenvectors */

	    i__1 = *n;
	    for (ii = 2; ii <= i__1; ++ii) {
		i__ = ii - 1;
		k = i__;
		p = d__[i__];
		i__2 = *n;
		for (j = ii; j <= i__2; ++j) {
		    if (d__[j] < p) {
			k = j;
			p = d__[j];
		    }
/* L30: */
		}
		if (k != i__) {
		    d__[k] = d__[i__];
		    d__[i__] = p;
		    sswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 
			    + 1], &c__1);
		}
/* L40: */
	    }
	}
    }

L50:
    work[1] = (real) lwmin;
    iwork[1] = liwmin;

    return 0;

/*     End of SSTEDC */

} /* sstedc_ */