OpenBLAS/lapack-netlib/SRC/zhbevd.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 doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static doublereal c_b13 = 1.;
static integer c__1 = 1;

/* > \brief <b> ZHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER 
matrices</b> */

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

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

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

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

/*       SUBROUTINE ZHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, */
/*                          LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO ) */

/*       CHARACTER          JOBZ, UPLO */
/*       INTEGER            INFO, KD, LDAB, LDZ, LIWORK, LRWORK, LWORK, N */
/*       INTEGER            IWORK( * ) */
/*       DOUBLE PRECISION   RWORK( * ), W( * ) */
/*       COMPLEX*16         AB( LDAB, * ), WORK( * ), Z( LDZ, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of */
/* > a complex Hermitian band matrix A.  If eigenvectors are desired, it */
/* > uses a divide and conquer algorithm. */
/* > */
/* > The divide and conquer algorithm 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. */
/* > \endverbatim */

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

/* > \param[in] JOBZ */
/* > \verbatim */
/* >          JOBZ is CHARACTER*1 */
/* >          = 'N':  Compute eigenvalues only; */
/* >          = 'V':  Compute eigenvalues and eigenvectors. */
/* > \endverbatim */
/* > */
/* > \param[in] UPLO */
/* > \verbatim */
/* >          UPLO is CHARACTER*1 */
/* >          = 'U':  Upper triangle of A is stored; */
/* >          = 'L':  Lower triangle of A is stored. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix A.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KD */
/* > \verbatim */
/* >          KD is INTEGER */
/* >          The number of superdiagonals of the matrix A if UPLO = 'U', */
/* >          or the number of subdiagonals if UPLO = 'L'.  KD >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] AB */
/* > \verbatim */
/* >          AB is COMPLEX*16 array, dimension (LDAB, N) */
/* >          On entry, the upper or lower triangle of the Hermitian band */
/* >          matrix A, stored in the first KD+1 rows of the array.  The */
/* >          j-th column of A is stored in the j-th column of the array AB */
/* >          as follows: */
/* >          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
/* >          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=f2cmin(n,j+kd). */
/* > */
/* >          On exit, AB is overwritten by values generated during the */
/* >          reduction to tridiagonal form.  If UPLO = 'U', the first */
/* >          superdiagonal and the diagonal of the tridiagonal matrix T */
/* >          are returned in rows KD and KD+1 of AB, and if UPLO = 'L', */
/* >          the diagonal and first subdiagonal of T are returned in the */
/* >          first two rows of AB. */
/* > \endverbatim */
/* > */
/* > \param[in] LDAB */
/* > \verbatim */
/* >          LDAB is INTEGER */
/* >          The leading dimension of the array AB.  LDAB >= KD + 1. */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* >          W is DOUBLE PRECISION array, dimension (N) */
/* >          If INFO = 0, the eigenvalues in ascending order. */
/* > \endverbatim */
/* > */
/* > \param[out] Z */
/* > \verbatim */
/* >          Z is COMPLEX*16 array, dimension (LDZ, N) */
/* >          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal */
/* >          eigenvectors of the matrix A, with the i-th column of Z */
/* >          holding the eigenvector associated with W(i). */
/* >          If JOBZ = '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 */
/* >          JOBZ = 'V', LDZ >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is COMPLEX*16 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 N <= 1,               LWORK must be at least 1. */
/* >          If JOBZ = 'N' and N > 1, LWORK must be at least N. */
/* >          If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2. */
/* > */
/* >          If LWORK = -1, then a workspace query is assumed; the routine */
/* >          only calculates the optimal sizes of the WORK, RWORK and */
/* >          IWORK arrays, returns these values as the first entries of */
/* >          the WORK, RWORK and IWORK arrays, and no error message */
/* >          related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* >          RWORK is DOUBLE PRECISION array, */
/* >                                         dimension (LRWORK) */
/* >          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LRWORK */
/* > \verbatim */
/* >          LRWORK is INTEGER */
/* >          The dimension of array RWORK. */
/* >          If N <= 1,               LRWORK must be at least 1. */
/* >          If JOBZ = 'N' and N > 1, LRWORK must be at least N. */
/* >          If JOBZ = 'V' and N > 1, LRWORK must be at least */
/* >                        1 + 5*N + 2*N**2. */
/* > */
/* >          If LRWORK = -1, then a workspace query is assumed; the */
/* >          routine only calculates the optimal sizes of the WORK, RWORK */
/* >          and IWORK arrays, returns these values as the first entries */
/* >          of the WORK, RWORK and IWORK arrays, and no error message */
/* >          related to LWORK or LRWORK or LIWORK 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 array IWORK. */
/* >          If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. */
/* >          If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N . */
/* > */
/* >          If LIWORK = -1, then a workspace query is assumed; the */
/* >          routine only calculates the optimal sizes of the WORK, RWORK */
/* >          and IWORK arrays, returns these values as the first entries */
/* >          of the WORK, RWORK and IWORK arrays, and no error message */
/* >          related to LWORK or LRWORK or 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:  if INFO = i, the algorithm failed to converge; i */
/* >                off-diagonal elements of an intermediate tridiagonal */
/* >                form did not converge to zero. */
/* > \endverbatim */

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

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

/* > \date December 2016 */

/* > \ingroup complex16OTHEReigen */

/*  ===================================================================== */
/* Subroutine */ void zhbevd_(char *jobz, char *uplo, integer *n, integer *kd, 
	doublecomplex *ab, integer *ldab, doublereal *w, doublecomplex *z__, 
	integer *ldz, doublecomplex *work, integer *lwork, doublereal *rwork, 
	integer *lrwork, integer *iwork, integer *liwork, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, z_dim1, z_offset, i__1;
    doublereal d__1;

    /* Local variables */
    integer inde;
    doublereal anrm;
    integer imax;
    doublereal rmin, rmax;
    integer llwk2;
    extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    doublereal sigma;
    extern logical lsame_(char *, char *);
    integer iinfo;
    extern /* Subroutine */ void zgemm_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *);
    integer lwmin;
    logical lower;
    integer llrwk;
    logical wantz;
    integer indwk2;
    extern doublereal dlamch_(char *);
    integer iscale;
    doublereal safmin;
    extern doublereal zlanhb_(char *, char *, integer *, integer *, 
	    doublecomplex *, integer *, doublereal *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    doublereal bignum;
    extern /* Subroutine */ void dsterf_(integer *, doublereal *, doublereal *,
	     integer *), zlascl_(char *, integer *, integer *, doublereal *, 
	    doublereal *, integer *, integer *, doublecomplex *, integer *, 
	    integer *), zstedc_(char *, integer *, doublereal *, 
	    doublereal *, doublecomplex *, integer *, doublecomplex *, 
	    integer *, doublereal *, integer *, integer *, integer *, integer 
	    *), zhbtrd_(char *, char *, integer *, integer *, 
	    doublecomplex *, integer *, doublereal *, doublereal *, 
	    doublecomplex *, integer *, doublecomplex *, integer *);
    integer indwrk, liwmin;
    extern /* Subroutine */ void zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *);
    integer lrwmin;
    doublereal smlnum;
    logical lquery;
    doublereal eps;


/*  -- LAPACK driver 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 */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1 * 1;
    ab -= ab_offset;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --work;
    --rwork;
    --iwork;

    /* Function Body */
    wantz = lsame_(jobz, "V");
    lower = lsame_(uplo, "L");
    lquery = *lwork == -1 || *liwork == -1 || *lrwork == -1;

    *info = 0;
    if (*n <= 1) {
	lwmin = 1;
	lrwmin = 1;
	liwmin = 1;
    } else {
	if (wantz) {
/* Computing 2nd power */
	    i__1 = *n;
	    lwmin = i__1 * i__1 << 1;
/* Computing 2nd power */
	    i__1 = *n;
	    lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
	    liwmin = *n * 5 + 3;
	} else {
	    lwmin = *n;
	    lrwmin = *n;
	    liwmin = 1;
	}
    }
    if (! (wantz || lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (lower || lsame_(uplo, "U"))) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*kd < 0) {
	*info = -4;
    } else if (*ldab < *kd + 1) {
	*info = -6;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -9;
    }

    if (*info == 0) {
	work[1].r = (doublereal) lwmin, work[1].i = 0.;
	rwork[1] = (doublereal) lrwmin;
	iwork[1] = liwmin;

	if (*lwork < lwmin && ! lquery) {
	    *info = -11;
	} else if (*lrwork < lrwmin && ! lquery) {
	    *info = -13;
	} else if (*liwork < liwmin && ! lquery) {
	    *info = -15;
	}
    }

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

/*     Quick return if possible */

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

    if (*n == 1) {
	i__1 = ab_dim1 + 1;
	w[1] = ab[i__1].r;
	if (wantz) {
	    i__1 = z_dim1 + 1;
	    z__[i__1].r = 1., z__[i__1].i = 0.;
	}
	return;
    }

/*     Get machine constants. */

    safmin = dlamch_("Safe minimum");
    eps = dlamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = sqrt(smlnum);
    rmax = sqrt(bignum);

/*     Scale matrix to allowable range, if necessary. */

    anrm = zlanhb_("M", uplo, n, kd, &ab[ab_offset], ldab, &rwork[1]);
    iscale = 0;
    if (anrm > 0. && anrm < rmin) {
	iscale = 1;
	sigma = rmin / anrm;
    } else if (anrm > rmax) {
	iscale = 1;
	sigma = rmax / anrm;
    }
    if (iscale == 1) {
	if (lower) {
	    zlascl_("B", kd, kd, &c_b13, &sigma, n, n, &ab[ab_offset], ldab, 
		    info);
	} else {
	    zlascl_("Q", kd, kd, &c_b13, &sigma, n, n, &ab[ab_offset], ldab, 
		    info);
	}
    }

/*     Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form. */

    inde = 1;
    indwrk = inde + *n;
    indwk2 = *n * *n + 1;
    llwk2 = *lwork - indwk2 + 1;
    llrwk = *lrwork - indwrk + 1;
    zhbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &w[1], &rwork[inde], &
	    z__[z_offset], ldz, &work[1], &iinfo);

/*     For eigenvalues only, call DSTERF.  For eigenvectors, call ZSTEDC. */

    if (! wantz) {
	dsterf_(n, &w[1], &rwork[inde], info);
    } else {
	zstedc_("I", n, &w[1], &rwork[inde], &work[1], n, &work[indwk2], &
		llwk2, &rwork[indwrk], &llrwk, &iwork[1], liwork, info);
	zgemm_("N", "N", n, n, n, &c_b2, &z__[z_offset], ldz, &work[1], n, &
		c_b1, &work[indwk2], n);
	zlacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz);
    }

/*     If matrix was scaled, then rescale eigenvalues appropriately. */

    if (iscale == 1) {
	if (*info == 0) {
	    imax = *n;
	} else {
	    imax = *info - 1;
	}
	d__1 = 1. / sigma;
	dscal_(&imax, &d__1, &w[1], &c__1);
    }

    work[1].r = (doublereal) lwmin, work[1].i = 0.;
    rwork[1] = (doublereal) lrwmin;
    iwork[1] = liwmin;
    return;

/*     End of ZHBEVD */

} /* zhbevd_ */