OpenBLAS/lapack-netlib/SRC/dstein.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 integer c__2 = 2;
static integer c__1 = 1;
static integer c_n1 = -1;

/* > \brief \b DSTEIN */

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

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

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

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

/*       SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, */
/*                          IWORK, IFAIL, INFO ) */

/*       INTEGER            INFO, LDZ, M, N */
/*       INTEGER            IBLOCK( * ), IFAIL( * ), ISPLIT( * ), */
/*      $                   IWORK( * ) */
/*       DOUBLE PRECISION   D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DSTEIN computes the eigenvectors of a real symmetric tridiagonal */
/* > matrix T corresponding to specified eigenvalues, using inverse */
/* > iteration. */
/* > */
/* > The maximum number of iterations allowed for each eigenvector is */
/* > specified by an internal parameter MAXITS (currently set to 5). */
/* > \endverbatim */

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

/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] D */
/* > \verbatim */
/* >          D is DOUBLE PRECISION array, dimension (N) */
/* >          The n diagonal elements of the tridiagonal matrix T. */
/* > \endverbatim */
/* > */
/* > \param[in] E */
/* > \verbatim */
/* >          E is DOUBLE PRECISION array, dimension (N-1) */
/* >          The (n-1) subdiagonal elements of the tridiagonal matrix */
/* >          T, in elements 1 to N-1. */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The number of eigenvectors to be found.  0 <= M <= N. */
/* > \endverbatim */
/* > */
/* > \param[in] W */
/* > \verbatim */
/* >          W is DOUBLE PRECISION array, dimension (N) */
/* >          The first M elements of W contain the eigenvalues for */
/* >          which eigenvectors are to be computed.  The eigenvalues */
/* >          should be grouped by split-off block and ordered from */
/* >          smallest to largest within the block.  ( The output array */
/* >          W from DSTEBZ with ORDER = 'B' is expected here. ) */
/* > \endverbatim */
/* > */
/* > \param[in] IBLOCK */
/* > \verbatim */
/* >          IBLOCK is INTEGER array, dimension (N) */
/* >          The submatrix indices associated with the corresponding */
/* >          eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to */
/* >          the first submatrix from the top, =2 if W(i) belongs to */
/* >          the second submatrix, etc.  ( The output array IBLOCK */
/* >          from DSTEBZ is expected here. ) */
/* > \endverbatim */
/* > */
/* > \param[in] ISPLIT */
/* > \verbatim */
/* >          ISPLIT is INTEGER array, dimension (N) */
/* >          The splitting points, at which T breaks up into submatrices. */
/* >          The first submatrix consists of rows/columns 1 to */
/* >          ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 */
/* >          through ISPLIT( 2 ), etc. */
/* >          ( The output array ISPLIT from DSTEBZ is expected here. ) */
/* > \endverbatim */
/* > */
/* > \param[out] Z */
/* > \verbatim */
/* >          Z is DOUBLE PRECISION array, dimension (LDZ, M) */
/* >          The computed eigenvectors.  The eigenvector associated */
/* >          with the eigenvalue W(i) is stored in the i-th column of */
/* >          Z.  Any vector which fails to converge is set to its current */
/* >          iterate after MAXITS iterations. */
/* > \endverbatim */
/* > */
/* > \param[in] LDZ */
/* > \verbatim */
/* >          LDZ is INTEGER */
/* >          The leading dimension of the array Z.  LDZ >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is DOUBLE PRECISION array, dimension (5*N) */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] IFAIL */
/* > \verbatim */
/* >          IFAIL is INTEGER array, dimension (M) */
/* >          On normal exit, all elements of IFAIL are zero. */
/* >          If one or more eigenvectors fail to converge after */
/* >          MAXITS iterations, then their indices are stored in */
/* >          array IFAIL. */
/* > \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, then i eigenvectors failed to converge */
/* >               in MAXITS iterations.  Their indices are stored in */
/* >               array IFAIL. */
/* > \endverbatim */

/* > \par Internal Parameters: */
/*  ========================= */
/* > */
/* > \verbatim */
/* >  MAXITS  INTEGER, default = 5 */
/* >          The maximum number of iterations performed. */
/* > */
/* >  EXTRA   INTEGER, default = 2 */
/* >          The number of iterations performed after norm growth */
/* >          criterion is satisfied, should be at least 1. */
/* > \endverbatim */

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

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

/* > \date December 2016 */

/* > \ingroup doubleOTHERcomputational */

/*  ===================================================================== */
/* Subroutine */ void dstein_(integer *n, doublereal *d__, doublereal *e, 
	integer *m, doublereal *w, integer *iblock, integer *isplit, 
	doublereal *z__, integer *ldz, doublereal *work, integer *iwork, 
	integer *ifail, integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1, i__2, i__3;
    doublereal d__1, d__2, d__3, d__4, d__5;

    /* Local variables */
    integer jblk, nblk;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    integer jmax;
    extern doublereal dnrm2_(integer *, doublereal *, integer *);
    integer i__, j;
    extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    integer iseed[4], gpind, iinfo;
    extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    integer b1;
    extern /* Subroutine */ void daxpy_(integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *);
    integer j1;
    doublereal ortol;
    integer indrv1, indrv2, indrv3, indrv4, indrv5, bn;
    extern doublereal dlamch_(char *);
    extern /* Subroutine */ void dlagtf_(integer *, doublereal *, doublereal *,
	     doublereal *, doublereal *, doublereal *, doublereal *, integer *
	    , integer *);
    doublereal xj;
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern void dlagts_(
	    integer *, integer *, doublereal *, doublereal *, doublereal *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *);
    integer nrmchk;
    extern /* Subroutine */ void dlarnv_(integer *, integer *, integer *, 
	    doublereal *);
    integer blksiz;
    doublereal onenrm, dtpcrt, pertol, scl, eps, sep, nrm, tol;
    integer its;
    doublereal xjm, ztr, eps1;


/*  -- 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;
    --w;
    --iblock;
    --isplit;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --work;
    --iwork;
    --ifail;

    /* Function Body */
    *info = 0;
    i__1 = *m;
    for (i__ = 1; i__ <= i__1; ++i__) {
	ifail[i__] = 0;
/* L10: */
    }

    if (*n < 0) {
	*info = -1;
    } else if (*m < 0 || *m > *n) {
	*info = -4;
    } else if (*ldz < f2cmax(1,*n)) {
	*info = -9;
    } else {
	i__1 = *m;
	for (j = 2; j <= i__1; ++j) {
	    if (iblock[j] < iblock[j - 1]) {
		*info = -6;
		goto L30;
	    }
	    if (iblock[j] == iblock[j - 1] && w[j] < w[j - 1]) {
		*info = -5;
		goto L30;
	    }
/* L20: */
	}
L30:
	;
    }

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

/*     Quick return if possible */

    if (*n == 0 || *m == 0) {
	return;
    } else if (*n == 1) {
	z__[z_dim1 + 1] = 1.;
	return;
    }

/*     Get machine constants. */

    eps = dlamch_("Precision");

/*     Initialize seed for random number generator DLARNV. */

    for (i__ = 1; i__ <= 4; ++i__) {
	iseed[i__ - 1] = 1;
/* L40: */
    }

/*     Initialize pointers. */

    indrv1 = 0;
    indrv2 = indrv1 + *n;
    indrv3 = indrv2 + *n;
    indrv4 = indrv3 + *n;
    indrv5 = indrv4 + *n;

/*     Compute eigenvectors of matrix blocks. */

    j1 = 1;
    i__1 = iblock[*m];
    for (nblk = 1; nblk <= i__1; ++nblk) {

/*        Find starting and ending indices of block nblk. */

	if (nblk == 1) {
	    b1 = 1;
	} else {
	    b1 = isplit[nblk - 1] + 1;
	}
	bn = isplit[nblk];
	blksiz = bn - b1 + 1;
	if (blksiz == 1) {
	    goto L60;
	}
	gpind = j1;

/*        Compute reorthogonalization criterion and stopping criterion. */

	onenrm = (d__1 = d__[b1], abs(d__1)) + (d__2 = e[b1], abs(d__2));
/* Computing MAX */
	d__3 = onenrm, d__4 = (d__1 = d__[bn], abs(d__1)) + (d__2 = e[bn - 1],
		 abs(d__2));
	onenrm = f2cmax(d__3,d__4);
	i__2 = bn - 1;
	for (i__ = b1 + 1; i__ <= i__2; ++i__) {
/* Computing MAX */
	    d__4 = onenrm, d__5 = (d__1 = d__[i__], abs(d__1)) + (d__2 = e[
		    i__ - 1], abs(d__2)) + (d__3 = e[i__], abs(d__3));
	    onenrm = f2cmax(d__4,d__5);
/* L50: */
	}
	ortol = onenrm * .001;

	dtpcrt = sqrt(.1 / blksiz);

/*        Loop through eigenvalues of block nblk. */

L60:
	jblk = 0;
	i__2 = *m;
	for (j = j1; j <= i__2; ++j) {
	    if (iblock[j] != nblk) {
		j1 = j;
		goto L160;
	    }
	    ++jblk;
	    xj = w[j];

/*           Skip all the work if the block size is one. */

	    if (blksiz == 1) {
		work[indrv1 + 1] = 1.;
		goto L120;
	    }

/*           If eigenvalues j and j-1 are too close, add a relatively */
/*           small perturbation. */

	    if (jblk > 1) {
		eps1 = (d__1 = eps * xj, abs(d__1));
		pertol = eps1 * 10.;
		sep = xj - xjm;
		if (sep < pertol) {
		    xj = xjm + pertol;
		}
	    }

	    its = 0;
	    nrmchk = 0;

/*           Get random starting vector. */

	    dlarnv_(&c__2, iseed, &blksiz, &work[indrv1 + 1]);

/*           Copy the matrix T so it won't be destroyed in factorization. */

	    dcopy_(&blksiz, &d__[b1], &c__1, &work[indrv4 + 1], &c__1);
	    i__3 = blksiz - 1;
	    dcopy_(&i__3, &e[b1], &c__1, &work[indrv2 + 2], &c__1);
	    i__3 = blksiz - 1;
	    dcopy_(&i__3, &e[b1], &c__1, &work[indrv3 + 1], &c__1);

/*           Compute LU factors with partial pivoting  ( PT = LU ) */

	    tol = 0.;
	    dlagtf_(&blksiz, &work[indrv4 + 1], &xj, &work[indrv2 + 2], &work[
		    indrv3 + 1], &tol, &work[indrv5 + 1], &iwork[1], &iinfo);

/*           Update iteration count. */

L70:
	    ++its;
	    if (its > 5) {
		goto L100;
	    }

/*           Normalize and scale the righthand side vector Pb. */

	    jmax = idamax_(&blksiz, &work[indrv1 + 1], &c__1);
/* Computing MAX */
	    d__3 = eps, d__4 = (d__1 = work[indrv4 + blksiz], abs(d__1));
	    scl = blksiz * onenrm * f2cmax(d__3,d__4) / (d__2 = work[indrv1 + 
		    jmax], abs(d__2));
	    dscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1);

/*           Solve the system LU = Pb. */

	    dlagts_(&c_n1, &blksiz, &work[indrv4 + 1], &work[indrv2 + 2], &
		    work[indrv3 + 1], &work[indrv5 + 1], &iwork[1], &work[
		    indrv1 + 1], &tol, &iinfo);

/*           Reorthogonalize by modified Gram-Schmidt if eigenvalues are */
/*           close enough. */

	    if (jblk == 1) {
		goto L90;
	    }
	    if ((d__1 = xj - xjm, abs(d__1)) > ortol) {
		gpind = j;
	    }
	    if (gpind != j) {
		i__3 = j - 1;
		for (i__ = gpind; i__ <= i__3; ++i__) {
		    ztr = -ddot_(&blksiz, &work[indrv1 + 1], &c__1, &z__[b1 + 
			    i__ * z_dim1], &c__1);
		    daxpy_(&blksiz, &ztr, &z__[b1 + i__ * z_dim1], &c__1, &
			    work[indrv1 + 1], &c__1);
/* L80: */
		}
	    }

/*           Check the infinity norm of the iterate. */

L90:
	    jmax = idamax_(&blksiz, &work[indrv1 + 1], &c__1);
	    nrm = (d__1 = work[indrv1 + jmax], abs(d__1));

/*           Continue for additional iterations after norm reaches */
/*           stopping criterion. */

	    if (nrm < dtpcrt) {
		goto L70;
	    }
	    ++nrmchk;
	    if (nrmchk < 3) {
		goto L70;
	    }

	    goto L110;

/*           If stopping criterion was not satisfied, update info and */
/*           store eigenvector number in array ifail. */

L100:
	    ++(*info);
	    ifail[*info] = j;

/*           Accept iterate as jth eigenvector. */

L110:
	    scl = 1. / dnrm2_(&blksiz, &work[indrv1 + 1], &c__1);
	    jmax = idamax_(&blksiz, &work[indrv1 + 1], &c__1);
	    if (work[indrv1 + jmax] < 0.) {
		scl = -scl;
	    }
	    dscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1);
L120:
	    i__3 = *n;
	    for (i__ = 1; i__ <= i__3; ++i__) {
		z__[i__ + j * z_dim1] = 0.;
/* L130: */
	    }
	    i__3 = blksiz;
	    for (i__ = 1; i__ <= i__3; ++i__) {
		z__[b1 + i__ - 1 + j * z_dim1] = work[indrv1 + i__];
/* L140: */
	    }

/*           Save the shift to check eigenvalue spacing at next */
/*           iteration. */

	    xjm = xj;

/* L150: */
	}
L160:
	;
    }

    return;

/*     End of DSTEIN */

} /* dstein_ */