OpenBLAS/lapack-netlib/SRC/dlaed7.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__2 = 2;
static integer c__1 = 1;
static doublereal c_b10 = 1.;
static doublereal c_b11 = 0.;
static integer c_n1 = -1;

/* > \brief \b DLAED7 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification
 by a rank-one symmetric matrix. Used when the original matrix is dense. */

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

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

/* > \htmlonly */
/* > Download DLAED7 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed7.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed7.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed7.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

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

/*       SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, */
/*                          LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, */
/*                          PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, */
/*                          INFO ) */

/*       INTEGER            CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, */
/*      $                   QSIZ, TLVLS */
/*       DOUBLE PRECISION   RHO */
/*       INTEGER            GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), */
/*      $                   IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) */
/*       DOUBLE PRECISION   D( * ), GIVNUM( 2, * ), Q( LDQ, * ), */
/*      $                   QSTORE( * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLAED7 computes the updated eigensystem of a diagonal */
/* > matrix after modification by a rank-one symmetric matrix. This */
/* > routine is used only for the eigenproblem which requires all */
/* > eigenvalues and optionally eigenvectors of a dense symmetric matrix */
/* > that has been reduced to tridiagonal form.  DLAED1 handles */
/* > the case in which all eigenvalues and eigenvectors of a symmetric */
/* > tridiagonal matrix are desired. */
/* > */
/* >   T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) */
/* > */
/* >    where Z = Q**Tu, u is a vector of length N with ones in the */
/* >    CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */
/* > */
/* >    The eigenvectors of the original matrix are stored in Q, and the */
/* >    eigenvalues are in D.  The algorithm consists of three stages: */
/* > */
/* >       The first stage consists of deflating the size of the problem */
/* >       when there are multiple eigenvalues or if there is a zero in */
/* >       the Z vector.  For each such occurrence the dimension of the */
/* >       secular equation problem is reduced by one.  This stage is */
/* >       performed by the routine DLAED8. */
/* > */
/* >       The second stage consists of calculating the updated */
/* >       eigenvalues. This is done by finding the roots of the secular */
/* >       equation via the routine DLAED4 (as called by DLAED9). */
/* >       This routine also calculates the eigenvectors of the current */
/* >       problem. */
/* > */
/* >       The final stage consists of computing the updated eigenvectors */
/* >       directly using the updated eigenvalues.  The eigenvectors for */
/* >       the current problem are multiplied with the eigenvectors from */
/* >       the overall problem. */
/* > \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. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >         The dimension of the symmetric tridiagonal matrix.  N >= 0. */
/* > \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] TLVLS */
/* > \verbatim */
/* >          TLVLS is INTEGER */
/* >         The total number of merging levels in the overall divide and */
/* >         conquer tree. */
/* > \endverbatim */
/* > */
/* > \param[in] CURLVL */
/* > \verbatim */
/* >          CURLVL is INTEGER */
/* >         The current level in the overall merge routine, */
/* >         0 <= CURLVL <= TLVLS. */
/* > \endverbatim */
/* > */
/* > \param[in] CURPBM */
/* > \verbatim */
/* >          CURPBM is INTEGER */
/* >         The current problem in the current level in the overall */
/* >         merge routine (counting from upper left to lower right). */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* >          D is DOUBLE PRECISION array, dimension (N) */
/* >         On entry, the eigenvalues of the rank-1-perturbed matrix. */
/* >         On exit, the eigenvalues of the repaired matrix. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Q */
/* > \verbatim */
/* >          Q is DOUBLE PRECISION array, dimension (LDQ, N) */
/* >         On entry, the eigenvectors of the rank-1-perturbed matrix. */
/* >         On exit, the eigenvectors of the repaired tridiagonal matrix. */
/* > \endverbatim */
/* > */
/* > \param[in] LDQ */
/* > \verbatim */
/* >          LDQ is INTEGER */
/* >         The leading dimension of the array Q.  LDQ >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] INDXQ */
/* > \verbatim */
/* >          INDXQ is INTEGER array, dimension (N) */
/* >         The permutation which will reintegrate the subproblem just */
/* >         solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) */
/* >         will be in ascending order. */
/* > \endverbatim */
/* > */
/* > \param[in] RHO */
/* > \verbatim */
/* >          RHO is DOUBLE PRECISION */
/* >         The subdiagonal element used to create the rank-1 */
/* >         modification. */
/* > \endverbatim */
/* > */
/* > \param[in] CUTPNT */
/* > \verbatim */
/* >          CUTPNT is INTEGER */
/* >         Contains the location of the last eigenvalue in the leading */
/* >         sub-matrix.  f2cmin(1,N) <= CUTPNT <= N. */
/* > \endverbatim */
/* > */
/* > \param[in,out] QSTORE */
/* > \verbatim */
/* >          QSTORE is DOUBLE PRECISION array, dimension (N**2+1) */
/* >         Stores eigenvectors of submatrices encountered during */
/* >         divide and conquer, packed together. QPTR points to */
/* >         beginning of the submatrices. */
/* > \endverbatim */
/* > */
/* > \param[in,out] QPTR */
/* > \verbatim */
/* >          QPTR is INTEGER array, dimension (N+2) */
/* >         List of indices pointing to beginning of submatrices stored */
/* >         in QSTORE. The submatrices are numbered starting at the */
/* >         bottom left of the divide and conquer tree, from left to */
/* >         right and bottom to top. */
/* > \endverbatim */
/* > */
/* > \param[in] PRMPTR */
/* > \verbatim */
/* >          PRMPTR is INTEGER array, dimension (N lg N) */
/* >         Contains a list of pointers which indicate where in PERM a */
/* >         level's permutation is stored.  PRMPTR(i+1) - PRMPTR(i) */
/* >         indicates the size of the permutation and also the size of */
/* >         the full, non-deflated problem. */
/* > \endverbatim */
/* > */
/* > \param[in] PERM */
/* > \verbatim */
/* >          PERM is INTEGER array, dimension (N lg N) */
/* >         Contains the permutations (from deflation and sorting) to be */
/* >         applied to each eigenblock. */
/* > \endverbatim */
/* > */
/* > \param[in] GIVPTR */
/* > \verbatim */
/* >          GIVPTR is INTEGER array, dimension (N lg N) */
/* >         Contains a list of pointers which indicate where in GIVCOL a */
/* >         level's Givens rotations are stored.  GIVPTR(i+1) - GIVPTR(i) */
/* >         indicates the number of Givens rotations. */
/* > \endverbatim */
/* > */
/* > \param[in] GIVCOL */
/* > \verbatim */
/* >          GIVCOL is INTEGER array, dimension (2, N lg N) */
/* >         Each pair of numbers indicates a pair of columns to take place */
/* >         in a Givens rotation. */
/* > \endverbatim */
/* > */
/* > \param[in] GIVNUM */
/* > \verbatim */
/* >          GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) */
/* >         Each number indicates the S value to be used in the */
/* >         corresponding Givens rotation. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is DOUBLE PRECISION array, dimension (3*N+2*QSIZ*N) */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (4*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:  if INFO = 1, an eigenvalue did not converge */
/* > \endverbatim */

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

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

/* > \date June 2016 */

/* > \ingroup auxOTHERcomputational */

/* > \par Contributors: */
/*  ================== */
/* > */
/* > Jeff Rutter, Computer Science Division, University of California */
/* > at Berkeley, USA */

/*  ===================================================================== */
/* Subroutine */ void dlaed7_(integer *icompq, integer *n, integer *qsiz, 
	integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, 
	doublereal *q, integer *ldq, integer *indxq, doublereal *rho, integer 
	*cutpnt, doublereal *qstore, integer *qptr, integer *prmptr, integer *
	perm, integer *givptr, integer *givcol, doublereal *givnum, 
	doublereal *work, integer *iwork, integer *info)
{
    /* System generated locals */
    integer q_dim1, q_offset, i__1, i__2;

    /* Local variables */
    integer indx, curr, i__, k;
    extern /* Subroutine */ void dgemm_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *);
    integer indxc, indxp, n1, n2;
    extern /* Subroutine */ void dlaed8_(integer *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, doublereal *,
	     integer *, doublereal *, integer *, integer *, integer *, 
	    doublereal *, integer *, integer *, integer *), dlaed9_(integer *,
	     integer *, integer *, integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, doublereal *, doublereal *, doublereal *,
	     integer *, integer *), dlaeda_(integer *, integer *, integer *, 
	    integer *, integer *, integer *, integer *, integer *, doublereal 
	    *, doublereal *, integer *, doublereal *, doublereal *, integer *)
	    ;
    integer idlmda, is, iw, iz;
    extern /* Subroutine */ void dlamrg_(integer *, integer *, doublereal *, 
	    integer *, integer *, integer *);
    extern int xerbla_(char *, integer *, ftnlen);
    integer coltyp, iq2, ptr, ldq2;


/*  -- 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..-- */
/*     June 2016 */


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


/*     Test the input parameters. */

    /* Parameter adjustments */
    --d__;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    --indxq;
    --qstore;
    --qptr;
    --prmptr;
    --perm;
    --givptr;
    givcol -= 3;
    givnum -= 3;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;

    if (*icompq < 0 || *icompq > 1) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*icompq == 1 && *qsiz < *n) {
	*info = -3;
    } else if (*ldq < f2cmax(1,*n)) {
	*info = -9;
    } else if (f2cmin(1,*n) > *cutpnt || *n < *cutpnt) {
	*info = -12;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DLAED7", &i__1, (ftnlen)6);
	return;
    }

/*     Quick return if possible */

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

/*     The following values are for bookkeeping purposes only.  They are */
/*     integer pointers which indicate the portion of the workspace */
/*     used by a particular array in DLAED8 and DLAED9. */

    if (*icompq == 1) {
	ldq2 = *qsiz;
    } else {
	ldq2 = *n;
    }

    iz = 1;
    idlmda = iz + *n;
    iw = idlmda + *n;
    iq2 = iw + *n;
    is = iq2 + *n * ldq2;

    indx = 1;
    indxc = indx + *n;
    coltyp = indxc + *n;
    indxp = coltyp + *n;

/*     Form the z-vector which consists of the last row of Q_1 and the */
/*     first row of Q_2. */

    ptr = pow_ii(c__2, *tlvls) + 1;
    i__1 = *curlvl - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {
	i__2 = *tlvls - i__;
	ptr += pow_ii(c__2, i__2);
/* L10: */
    }
    curr = ptr + *curpbm;
    dlaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], &
	    givcol[3], &givnum[3], &qstore[1], &qptr[1], &work[iz], &work[iz 
	    + *n], info);

/*     When solving the final problem, we no longer need the stored data, */
/*     so we will overwrite the data from this level onto the previously */
/*     used storage space. */

    if (*curlvl == *tlvls) {
	qptr[curr] = 1;
	prmptr[curr] = 1;
	givptr[curr] = 1;
    }

/*     Sort and Deflate eigenvalues. */

    dlaed8_(icompq, &k, n, qsiz, &d__[1], &q[q_offset], ldq, &indxq[1], rho, 
	    cutpnt, &work[iz], &work[idlmda], &work[iq2], &ldq2, &work[iw], &
	    perm[prmptr[curr]], &givptr[curr + 1], &givcol[(givptr[curr] << 1)
	     + 1], &givnum[(givptr[curr] << 1) + 1], &iwork[indxp], &iwork[
	    indx], info);
    prmptr[curr + 1] = prmptr[curr] + *n;
    givptr[curr + 1] += givptr[curr];

/*     Solve Secular Equation. */

    if (k != 0) {
	dlaed9_(&k, &c__1, &k, n, &d__[1], &work[is], &k, rho, &work[idlmda], 
		&work[iw], &qstore[qptr[curr]], &k, info);
	if (*info != 0) {
	    goto L30;
	}
	if (*icompq == 1) {
	    dgemm_("N", "N", qsiz, &k, &k, &c_b10, &work[iq2], &ldq2, &qstore[
		    qptr[curr]], &k, &c_b11, &q[q_offset], ldq);
	}
/* Computing 2nd power */
	i__1 = k;
	qptr[curr + 1] = qptr[curr] + i__1 * i__1;

/*     Prepare the INDXQ sorting permutation. */

	n1 = k;
	n2 = *n - k;
	dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]);
    } else {
	qptr[curr + 1] = qptr[curr];
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    indxq[i__] = i__;
/* L20: */
	}
    }

L30:
    return;

/*     End of DLAED7 */

} /* dlaed7_ */