OpenBLAS/lapack-netlib/SRC/dsteqr.c

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

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

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

typedef blasint integer;

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

typedef char logical1;
typedef char integer1;

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

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

/* I/O stuff */

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

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

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

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

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

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

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

#define VOID void

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

typedef union Multitype Multitype;

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

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

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

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

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


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

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




/* Table of constant values */

static doublereal c_b9 = 0.;
static doublereal c_b10 = 1.;
static integer c__0 = 0;
static integer c__1 = 1;
static integer c__2 = 2;

/* > \brief \b DSTEQR */

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

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

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

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

/*       SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) */

/*       CHARACTER          COMPZ */
/*       INTEGER            INFO, LDZ, N */
/*       DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DSTEQR computes all eigenvalues and, optionally, eigenvectors of a */
/* > symmetric tridiagonal matrix using the implicit QL or QR method. */
/* > The eigenvectors of a full or band symmetric matrix can also be found */
/* > if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to */
/* > tridiagonal form. */
/* > \endverbatim */

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

/* > \param[in] COMPZ */
/* > \verbatim */
/* >          COMPZ is CHARACTER*1 */
/* >          = 'N':  Compute eigenvalues only. */
/* >          = 'V':  Compute eigenvalues and eigenvectors of the original */
/* >                  symmetric matrix.  On entry, Z must contain the */
/* >                  orthogonal matrix used to reduce the original matrix */
/* >                  to tridiagonal form. */
/* >          = 'I':  Compute eigenvalues and eigenvectors of the */
/* >                  tridiagonal matrix.  Z is initialized to the identity */
/* >                  matrix. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* >          D is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N-1) */
/* >          On entry, the (n-1) subdiagonal elements of the tridiagonal */
/* >          matrix. */
/* >          On exit, E has been destroyed. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Z */
/* > \verbatim */
/* >          Z is DOUBLE PRECISION 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, and if */
/* >          eigenvectors are desired, then  LDZ >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is DOUBLE PRECISION array, dimension (f2cmax(1,2*N-2)) */
/* >          If COMPZ = 'N', then WORK is not referenced. */
/* > \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 has failed to find all the eigenvalues in */
/* >                a total of 30*N iterations; if INFO = i, then i */
/* >                elements of E have not converged to zero; on exit, D */
/* >                and E contain the elements of a symmetric tridiagonal */
/* >                matrix which is orthogonally similar to the original */
/* >                matrix. */
/* > \endverbatim */

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

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

/* > \date December 2016 */

/* > \ingroup auxOTHERcomputational */

/*  ===================================================================== */
/* Subroutine */ void dsteqr_(char *compz, integer *n, doublereal *d__, 
	doublereal *e, doublereal *z__, integer *ldz, doublereal *work, 
	integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1, i__2;
    doublereal d__1, d__2;

    /* Local variables */
    integer lend, jtot;
    extern /* Subroutine */ void dlae2_(doublereal *, doublereal *, doublereal 
	    *, doublereal *, doublereal *);
    doublereal b, c__, f, g;
    integer i__, j, k, l, m;
    doublereal p, r__, s;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ void dlasr_(char *, char *, char *, integer *, 
	    integer *, doublereal *, doublereal *, doublereal *, integer *);
    doublereal anorm;
    extern /* Subroutine */ void dswap_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    integer l1;
    extern /* Subroutine */ void dlaev2_(doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, 
	    doublereal *);
    integer lendm1, lendp1;
    extern doublereal dlapy2_(doublereal *, doublereal *);
    integer ii;
    extern doublereal dlamch_(char *);
    integer mm, iscale;
    extern /* Subroutine */ void dlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, integer *), dlaset_(char *, integer *, integer 
	    *, doublereal *, doublereal *, doublereal *, integer *);
    doublereal safmin;
    extern /* Subroutine */ void dlartg_(doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *);
    doublereal safmax;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
    extern /* Subroutine */ void dlasrt_(char *, integer *, doublereal *, 
	    integer *);
    integer lendsv;
    doublereal ssfmin;
    integer nmaxit, icompz;
    doublereal ssfmax;
    integer lm1, mm1, nm1;
    doublereal rt1, rt2, eps;
    integer lsv;
    doublereal tst, eps2;


/*  -- 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;

    /* Function Body */
    *info = 0;

    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) {
	i__1 = -(*info);
	xerbla_("DSTEQR", &i__1, (ftnlen)6);
	return;
    }

/*     Quick return if possible */

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

    if (*n == 1) {
	if (icompz == 2) {
	    z__[z_dim1 + 1] = 1.;
	}
	return;
    }

/*     Determine the unit roundoff and over/underflow thresholds. */

    eps = dlamch_("E");
/* Computing 2nd power */
    d__1 = eps;
    eps2 = d__1 * d__1;
    safmin = dlamch_("S");
    safmax = 1. / safmin;
    ssfmax = sqrt(safmax) / 3.;
    ssfmin = sqrt(safmin) / eps2;

/*     Compute the eigenvalues and eigenvectors of the tridiagonal */
/*     matrix. */

    if (icompz == 2) {
	dlaset_("Full", n, n, &c_b9, &c_b10, &z__[z_offset], ldz);
    }

    nmaxit = *n * 30;
    jtot = 0;

/*     Determine where the matrix splits and choose QL or QR iteration */
/*     for each block, according to whether top or bottom diagonal */
/*     element is smaller. */

    l1 = 1;
    nm1 = *n - 1;

L10:
    if (l1 > *n) {
	goto L160;
    }
    if (l1 > 1) {
	e[l1 - 1] = 0.;
    }
    if (l1 <= nm1) {
	i__1 = nm1;
	for (m = l1; m <= i__1; ++m) {
	    tst = (d__1 = e[m], abs(d__1));
	    if (tst == 0.) {
		goto L30;
	    }
	    if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m 
		    + 1], abs(d__2))) * eps) {
		e[m] = 0.;
		goto L30;
	    }
/* L20: */
	}
    }
    m = *n;

L30:
    l = l1;
    lsv = l;
    lend = m;
    lendsv = lend;
    l1 = m + 1;
    if (lend == l) {
	goto L10;
    }

/*     Scale submatrix in rows and columns L to LEND */

    i__1 = lend - l + 1;
    anorm = dlanst_("M", &i__1, &d__[l], &e[l]);
    iscale = 0;
    if (anorm == 0.) {
	goto L10;
    }
    if (anorm > ssfmax) {
	iscale = 1;
	i__1 = lend - l + 1;
	dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, 
		info);
	i__1 = lend - l;
	dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, 
		info);
    } else if (anorm < ssfmin) {
	iscale = 2;
	i__1 = lend - l + 1;
	dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, 
		info);
	i__1 = lend - l;
	dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, 
		info);
    }

/*     Choose between QL and QR iteration */

    if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) {
	lend = lsv;
	l = lendsv;
    }

    if (lend > l) {

/*        QL Iteration */

/*        Look for small subdiagonal element. */

L40:
	if (l != lend) {
	    lendm1 = lend - 1;
	    i__1 = lendm1;
	    for (m = l; m <= i__1; ++m) {
/* Computing 2nd power */
		d__2 = (d__1 = e[m], abs(d__1));
		tst = d__2 * d__2;
		if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m 
			+ 1], abs(d__2)) + safmin) {
		    goto L60;
		}
/* L50: */
	    }
	}

	m = lend;

L60:
	if (m < lend) {
	    e[m] = 0.;
	}
	p = d__[l];
	if (m == l) {
	    goto L80;
	}

/*        If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */
/*        to compute its eigensystem. */

	if (m == l + 1) {
	    if (icompz > 0) {
		dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s);
		work[l] = c__;
		work[*n - 1 + l] = s;
		dlasr_("R", "V", "B", n, &c__2, &work[l], &work[*n - 1 + l], &
			z__[l * z_dim1 + 1], ldz);
	    } else {
		dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2);
	    }
	    d__[l] = rt1;
	    d__[l + 1] = rt2;
	    e[l] = 0.;
	    l += 2;
	    if (l <= lend) {
		goto L40;
	    }
	    goto L140;
	}

	if (jtot == nmaxit) {
	    goto L140;
	}
	++jtot;

/*        Form shift. */

	g = (d__[l + 1] - p) / (e[l] * 2.);
	r__ = dlapy2_(&g, &c_b10);
	g = d__[m] - p + e[l] / (g + d_sign(&r__, &g));

	s = 1.;
	c__ = 1.;
	p = 0.;

/*        Inner loop */

	mm1 = m - 1;
	i__1 = l;
	for (i__ = mm1; i__ >= i__1; --i__) {
	    f = s * e[i__];
	    b = c__ * e[i__];
	    dlartg_(&g, &f, &c__, &s, &r__);
	    if (i__ != m - 1) {
		e[i__ + 1] = r__;
	    }
	    g = d__[i__ + 1] - p;
	    r__ = (d__[i__] - g) * s + c__ * 2. * b;
	    p = s * r__;
	    d__[i__ + 1] = g + p;
	    g = c__ * r__ - b;

/*           If eigenvectors are desired, then save rotations. */

	    if (icompz > 0) {
		work[i__] = c__;
		work[*n - 1 + i__] = -s;
	    }

/* L70: */
	}

/*        If eigenvectors are desired, then apply saved rotations. */

	if (icompz > 0) {
	    mm = m - l + 1;
	    dlasr_("R", "V", "B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l 
		    * z_dim1 + 1], ldz);
	}

	d__[l] -= p;
	e[l] = g;
	goto L40;

/*        Eigenvalue found. */

L80:
	d__[l] = p;

	++l;
	if (l <= lend) {
	    goto L40;
	}
	goto L140;

    } else {

/*        QR Iteration */

/*        Look for small superdiagonal element. */

L90:
	if (l != lend) {
	    lendp1 = lend + 1;
	    i__1 = lendp1;
	    for (m = l; m >= i__1; --m) {
/* Computing 2nd power */
		d__2 = (d__1 = e[m - 1], abs(d__1));
		tst = d__2 * d__2;
		if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m 
			- 1], abs(d__2)) + safmin) {
		    goto L110;
		}
/* L100: */
	    }
	}

	m = lend;

L110:
	if (m > lend) {
	    e[m - 1] = 0.;
	}
	p = d__[l];
	if (m == l) {
	    goto L130;
	}

/*        If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */
/*        to compute its eigensystem. */

	if (m == l - 1) {
	    if (icompz > 0) {
		dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s)
			;
		work[m] = c__;
		work[*n - 1 + m] = s;
		dlasr_("R", "V", "F", n, &c__2, &work[m], &work[*n - 1 + m], &
			z__[(l - 1) * z_dim1 + 1], ldz);
	    } else {
		dlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2);
	    }
	    d__[l - 1] = rt1;
	    d__[l] = rt2;
	    e[l - 1] = 0.;
	    l += -2;
	    if (l >= lend) {
		goto L90;
	    }
	    goto L140;
	}

	if (jtot == nmaxit) {
	    goto L140;
	}
	++jtot;

/*        Form shift. */

	g = (d__[l - 1] - p) / (e[l - 1] * 2.);
	r__ = dlapy2_(&g, &c_b10);
	g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g));

	s = 1.;
	c__ = 1.;
	p = 0.;

/*        Inner loop */

	lm1 = l - 1;
	i__1 = lm1;
	for (i__ = m; i__ <= i__1; ++i__) {
	    f = s * e[i__];
	    b = c__ * e[i__];
	    dlartg_(&g, &f, &c__, &s, &r__);
	    if (i__ != m) {
		e[i__ - 1] = r__;
	    }
	    g = d__[i__] - p;
	    r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b;
	    p = s * r__;
	    d__[i__] = g + p;
	    g = c__ * r__ - b;

/*           If eigenvectors are desired, then save rotations. */

	    if (icompz > 0) {
		work[i__] = c__;
		work[*n - 1 + i__] = s;
	    }

/* L120: */
	}

/*        If eigenvectors are desired, then apply saved rotations. */

	if (icompz > 0) {
	    mm = l - m + 1;
	    dlasr_("R", "V", "F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m 
		    * z_dim1 + 1], ldz);
	}

	d__[l] -= p;
	e[lm1] = g;
	goto L90;

/*        Eigenvalue found. */

L130:
	d__[l] = p;

	--l;
	if (l >= lend) {
	    goto L90;
	}
	goto L140;

    }

/*     Undo scaling if necessary */

L140:
    if (iscale == 1) {
	i__1 = lendsv - lsv + 1;
	dlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], 
		n, info);
	i__1 = lendsv - lsv;
	dlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, 
		info);
    } else if (iscale == 2) {
	i__1 = lendsv - lsv + 1;
	dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], 
		n, info);
	i__1 = lendsv - lsv;
	dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, 
		info);
    }

/*     Check for no convergence to an eigenvalue after a total */
/*     of N*MAXIT iterations. */

    if (jtot < nmaxit) {
	goto L10;
    }
    i__1 = *n - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {
	if (e[i__] != 0.) {
	    ++(*info);
	}
/* L150: */
    }
    goto L190;

/*     Order eigenvalues and eigenvectors. */

L160:
    if (icompz == 0) {

/*        Use Quick Sort */

	dlasrt_("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];
		}
/* L170: */
	    }
	    if (k != i__) {
		d__[k] = d__[i__];
		d__[i__] = p;
		dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1],
			 &c__1);
	    }
/* L180: */
	}
    }

L190:
    return;

/*     End of DSTEQR */

} /* dsteqr_ */