OpenBLAS/lapack-netlib/SRC/dlaed0.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 doublereal c_b23 = 1.;
static doublereal c_b24 = 0.;
static integer c__1 = 1;

/* > \brief \b DLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced 
symmetric tridiagonal matrix using the divide and conquer method. */

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

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

/* > \htmlonly */
/* > Download DLAED0 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed0.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed0.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed0.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

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

/*       SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, */
/*                          WORK, IWORK, INFO ) */

/*       INTEGER            ICOMPQ, INFO, LDQ, LDQS, N, QSIZ */
/*       INTEGER            IWORK( * ) */
/*       DOUBLE PRECISION   D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), */
/*      $                   WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLAED0 computes all eigenvalues and corresponding eigenvectors of a */
/* > symmetric tridiagonal matrix using the divide and conquer method. */
/* > \endverbatim */

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

/* > \param[in] ICOMPQ */
/* > \verbatim */
/* >          ICOMPQ is INTEGER */
/* >          = 0:  Compute eigenvalues only. */
/* >          = 1:  Compute eigenvectors of original dense symmetric matrix */
/* >                also.  On entry, Q contains the orthogonal matrix used */
/* >                to reduce the original matrix to tridiagonal form. */
/* >          = 2:  Compute eigenvalues and eigenvectors of tridiagonal */
/* >                matrix. */
/* > \endverbatim */
/* > */
/* > \param[in] QSIZ */
/* > \verbatim */
/* >          QSIZ is INTEGER */
/* >         The dimension of the orthogonal matrix used to reduce */
/* >         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1. */
/* > \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 DOUBLE PRECISION array, dimension (N) */
/* >         On entry, the main diagonal of the tridiagonal matrix. */
/* >         On exit, its eigenvalues. */
/* > \endverbatim */
/* > */
/* > \param[in] E */
/* > \verbatim */
/* >          E is DOUBLE PRECISION array, dimension (N-1) */
/* >         The off-diagonal elements of the tridiagonal matrix. */
/* >         On exit, E has been destroyed. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Q */
/* > \verbatim */
/* >          Q is DOUBLE PRECISION array, dimension (LDQ, N) */
/* >         On entry, Q must contain an N-by-N orthogonal matrix. */
/* >         If ICOMPQ = 0    Q is not referenced. */
/* >         If ICOMPQ = 1    On entry, Q is a subset of the columns of the */
/* >                          orthogonal matrix used to reduce the full */
/* >                          matrix to tridiagonal form corresponding to */
/* >                          the subset of the full matrix which is being */
/* >                          decomposed at this time. */
/* >         If ICOMPQ = 2    On entry, Q will be the identity matrix. */
/* >                          On exit, Q contains the eigenvectors of the */
/* >                          tridiagonal matrix. */
/* > \endverbatim */
/* > */
/* > \param[in] LDQ */
/* > \verbatim */
/* >          LDQ is INTEGER */
/* >         The leading dimension of the array Q.  If eigenvectors are */
/* >         desired, then  LDQ >= f2cmax(1,N).  In any case,  LDQ >= 1. */
/* > \endverbatim */
/* > */
/* > \param[out] QSTORE */
/* > \verbatim */
/* >          QSTORE is DOUBLE PRECISION array, dimension (LDQS, N) */
/* >         Referenced only when ICOMPQ = 1.  Used to store parts of */
/* >         the eigenvector matrix when the updating matrix multiplies */
/* >         take place. */
/* > \endverbatim */
/* > */
/* > \param[in] LDQS */
/* > \verbatim */
/* >          LDQS is INTEGER */
/* >         The leading dimension of the array QSTORE.  If ICOMPQ = 1, */
/* >         then  LDQS >= f2cmax(1,N).  In any case,  LDQS >= 1. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is DOUBLE PRECISION array, */
/* >         If ICOMPQ = 0 or 1, the dimension of WORK must be at least */
/* >                     1 + 3*N + 2*N*lg N + 3*N**2 */
/* >                     ( lg( N ) = smallest integer k */
/* >                                 such that 2^k >= N ) */
/* >         If ICOMPQ = 2, the dimension of WORK must be at least */
/* >                     4*N + N**2. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, */
/* >         If ICOMPQ = 0 or 1, the dimension of IWORK must be at least */
/* >                        6 + 6*N + 5*N*lg N. */
/* >                        ( lg( N ) = smallest integer k */
/* >                                    such that 2^k >= N ) */
/* >         If ICOMPQ = 2, the dimension of IWORK must be at least */
/* >                        3 + 5*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:  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 */

/*  ===================================================================== */
/* Subroutine */ int dlaed0_(integer *icompq, integer *qsiz, integer *n, 
	doublereal *d__, doublereal *e, doublereal *q, integer *ldq, 
	doublereal *qstore, integer *ldqs, doublereal *work, integer *iwork, 
	integer *info)
{
    /* System generated locals */
    integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2;
    doublereal d__1;

    /* Local variables */
    doublereal temp;
    integer curr, i__, j, k;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *);
    integer iperm;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    integer indxq, iwrem;
    extern /* Subroutine */ int dlaed1_(integer *, doublereal *, doublereal *,
	     integer *, integer *, doublereal *, integer *, doublereal *, 
	    integer *, integer *);
    integer iqptr;
    extern /* Subroutine */ int dlaed7_(integer *, integer *, integer *, 
	    integer *, integer *, integer *, doublereal *, doublereal *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    integer *, integer *, integer *, integer *, integer *, doublereal 
	    *, doublereal *, integer *, integer *);
    integer tlvls, iq;
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *);
    integer igivcl;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    integer igivnm, submat, curprb, subpbs, igivpt;
    extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *);
    integer curlvl, matsiz, iprmpt, smlsiz, lgn, msd2, smm1, spm1, spm2;


/*  -- 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;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    qstore_dim1 = *ldqs;
    qstore_offset = 1 + qstore_dim1 * 1;
    qstore -= qstore_offset;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;

    if (*icompq < 0 || *icompq > 2) {
	*info = -1;
    } else if (*icompq == 1 && *qsiz < f2cmax(0,*n)) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*ldq < f2cmax(1,*n)) {
	*info = -7;
    } else if (*ldqs < f2cmax(1,*n)) {
	*info = -9;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DLAED0", &i__1, (ftnlen)6);
	return 0;
    }

/*     Quick return if possible */

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

    smlsiz = ilaenv_(&c__9, "DLAED0", " ", &c__0, &c__0, &c__0, &c__0, (
	    ftnlen)6, (ftnlen)1);

/*     Determine the size and placement of the submatrices, and save in */
/*     the leading elements of IWORK. */

    iwork[1] = *n;
    subpbs = 1;
    tlvls = 0;
L10:
    if (iwork[subpbs] > smlsiz) {
	for (j = subpbs; j >= 1; --j) {
	    iwork[j * 2] = (iwork[j] + 1) / 2;
	    iwork[(j << 1) - 1] = iwork[j] / 2;
/* L20: */
	}
	++tlvls;
	subpbs <<= 1;
	goto L10;
    }
    i__1 = subpbs;
    for (j = 2; j <= i__1; ++j) {
	iwork[j] += iwork[j - 1];
/* L30: */
    }

/*     Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 */
/*     using rank-1 modifications (cuts). */

    spm1 = subpbs - 1;
    i__1 = spm1;
    for (i__ = 1; i__ <= i__1; ++i__) {
	submat = iwork[i__] + 1;
	smm1 = submat - 1;
	d__[smm1] -= (d__1 = e[smm1], abs(d__1));
	d__[submat] -= (d__1 = e[smm1], abs(d__1));
/* L40: */
    }

    indxq = (*n << 2) + 3;
    if (*icompq != 2) {

/*        Set up workspaces for eigenvalues only/accumulate new vectors */
/*        routine */

	temp = log((doublereal) (*n)) / log(2.);
	lgn = (integer) temp;
	if (pow_ii(c__2, lgn) < *n) {
	    ++lgn;
	}
	if (pow_ii(c__2, lgn) < *n) {
	    ++lgn;
	}
	iprmpt = indxq + *n + 1;
	iperm = iprmpt + *n * lgn;
	iqptr = iperm + *n * lgn;
	igivpt = iqptr + *n + 2;
	igivcl = igivpt + *n * lgn;

	igivnm = 1;
	iq = igivnm + (*n << 1) * lgn;
/* Computing 2nd power */
	i__1 = *n;
	iwrem = iq + i__1 * i__1 + 1;

/*        Initialize pointers */

	i__1 = subpbs;
	for (i__ = 0; i__ <= i__1; ++i__) {
	    iwork[iprmpt + i__] = 1;
	    iwork[igivpt + i__] = 1;
/* L50: */
	}
	iwork[iqptr] = 1;
    }

/*     Solve each submatrix eigenproblem at the bottom of the divide and */
/*     conquer tree. */

    curr = 0;
    i__1 = spm1;
    for (i__ = 0; i__ <= i__1; ++i__) {
	if (i__ == 0) {
	    submat = 1;
	    matsiz = iwork[1];
	} else {
	    submat = iwork[i__] + 1;
	    matsiz = iwork[i__ + 1] - iwork[i__];
	}
	if (*icompq == 2) {
	    dsteqr_("I", &matsiz, &d__[submat], &e[submat], &q[submat + 
		    submat * q_dim1], ldq, &work[1], info);
	    if (*info != 0) {
		goto L130;
	    }
	} else {
	    dsteqr_("I", &matsiz, &d__[submat], &e[submat], &work[iq - 1 + 
		    iwork[iqptr + curr]], &matsiz, &work[1], info);
	    if (*info != 0) {
		goto L130;
	    }
	    if (*icompq == 1) {
		dgemm_("N", "N", qsiz, &matsiz, &matsiz, &c_b23, &q[submat * 
			q_dim1 + 1], ldq, &work[iq - 1 + iwork[iqptr + curr]],
			 &matsiz, &c_b24, &qstore[submat * qstore_dim1 + 1], 
			ldqs);
	    }
/* Computing 2nd power */
	    i__2 = matsiz;
	    iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2;
	    ++curr;
	}
	k = 1;
	i__2 = iwork[i__ + 1];
	for (j = submat; j <= i__2; ++j) {
	    iwork[indxq + j] = k;
	    ++k;
/* L60: */
	}
/* L70: */
    }

/*     Successively merge eigensystems of adjacent submatrices */
/*     into eigensystem for the corresponding larger matrix. */

/*     while ( SUBPBS > 1 ) */

    curlvl = 1;
L80:
    if (subpbs > 1) {
	spm2 = subpbs - 2;
	i__1 = spm2;
	for (i__ = 0; i__ <= i__1; i__ += 2) {
	    if (i__ == 0) {
		submat = 1;
		matsiz = iwork[2];
		msd2 = iwork[1];
		curprb = 0;
	    } else {
		submat = iwork[i__] + 1;
		matsiz = iwork[i__ + 2] - iwork[i__];
		msd2 = matsiz / 2;
		++curprb;
	    }

/*     Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */
/*     into an eigensystem of size MATSIZ. */
/*     DLAED1 is used only for the full eigensystem of a tridiagonal */
/*     matrix. */
/*     DLAED7 handles the cases in which eigenvalues only or eigenvalues */
/*     and eigenvectors of a full symmetric matrix (which was reduced to */
/*     tridiagonal form) are desired. */

	    if (*icompq == 2) {
		dlaed1_(&matsiz, &d__[submat], &q[submat + submat * q_dim1], 
			ldq, &iwork[indxq + submat], &e[submat + msd2 - 1], &
			msd2, &work[1], &iwork[subpbs + 1], info);
	    } else {
		dlaed7_(icompq, &matsiz, qsiz, &tlvls, &curlvl, &curprb, &d__[
			submat], &qstore[submat * qstore_dim1 + 1], ldqs, &
			iwork[indxq + submat], &e[submat + msd2 - 1], &msd2, &
			work[iq], &iwork[iqptr], &iwork[iprmpt], &iwork[iperm]
			, &iwork[igivpt], &iwork[igivcl], &work[igivnm], &
			work[iwrem], &iwork[subpbs + 1], info);
	    }
	    if (*info != 0) {
		goto L130;
	    }
	    iwork[i__ / 2 + 1] = iwork[i__ + 2];
/* L90: */
	}
	subpbs /= 2;
	++curlvl;
	goto L80;
    }

/*     end while */

/*     Re-merge the eigenvalues/vectors which were deflated at the final */
/*     merge step. */

    if (*icompq == 1) {
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    j = iwork[indxq + i__];
	    work[i__] = d__[j];
	    dcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 
		    + 1], &c__1);
/* L100: */
	}
	dcopy_(n, &work[1], &c__1, &d__[1], &c__1);
    } else if (*icompq == 2) {
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    j = iwork[indxq + i__];
	    work[i__] = d__[j];
	    dcopy_(n, &q[j * q_dim1 + 1], &c__1, &work[*n * i__ + 1], &c__1);
/* L110: */
	}
	dcopy_(n, &work[1], &c__1, &d__[1], &c__1);
	dlacpy_("A", n, n, &work[*n + 1], n, &q[q_offset], ldq);
    } else {
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    j = iwork[indxq + i__];
	    work[i__] = d__[j];
/* L120: */
	}
	dcopy_(n, &work[1], &c__1, &d__[1], &c__1);
    }
    goto L140;

L130:
    *info = submat * (*n + 1) + submat + matsiz - 1;

L140:
    return 0;

/*     End of DLAED0 */

} /* dlaed0_ */