OpenBLAS/lapack-netlib/SRC/dlatrd.c

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

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

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

typedef blasint integer;

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

typedef char logical1;
typedef char integer1;

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

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

/* I/O stuff */

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

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

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

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

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

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

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

#define VOID void

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

typedef union Multitype Multitype;

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

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

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

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

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


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

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




/* Table of constant values */

static doublereal c_b5 = -1.;
static doublereal c_b6 = 1.;
static integer c__1 = 1;
static doublereal c_b16 = 0.;

/* > \brief \b DLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiago
nal form by an orthogonal similarity transformation. */

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

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

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

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

/*       SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) */

/*       CHARACTER          UPLO */
/*       INTEGER            LDA, LDW, N, NB */
/*       DOUBLE PRECISION   A( LDA, * ), E( * ), TAU( * ), W( LDW, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLATRD reduces NB rows and columns of a real symmetric matrix A to */
/* > symmetric tridiagonal form by an orthogonal similarity */
/* > transformation Q**T * A * Q, and returns the matrices V and W which are */
/* > needed to apply the transformation to the unreduced part of A. */
/* > */
/* > If UPLO = 'U', DLATRD reduces the last NB rows and columns of a */
/* > matrix, of which the upper triangle is supplied; */
/* > if UPLO = 'L', DLATRD reduces the first NB rows and columns of a */
/* > matrix, of which the lower triangle is supplied. */
/* > */
/* > This is an auxiliary routine called by DSYTRD. */
/* > \endverbatim */

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

/* > \param[in] UPLO */
/* > \verbatim */
/* >          UPLO is CHARACTER*1 */
/* >          Specifies whether the upper or lower triangular part of the */
/* >          symmetric matrix A is stored: */
/* >          = 'U': Upper triangular */
/* >          = 'L': Lower triangular */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] NB */
/* > \verbatim */
/* >          NB is INTEGER */
/* >          The number of rows and columns to be reduced. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is DOUBLE PRECISION array, dimension (LDA,N) */
/* >          On entry, the symmetric matrix A.  If UPLO = 'U', the leading */
/* >          n-by-n upper triangular part of A contains the upper */
/* >          triangular part of the matrix A, and the strictly lower */
/* >          triangular part of A is not referenced.  If UPLO = 'L', the */
/* >          leading n-by-n lower triangular part of A contains the lower */
/* >          triangular part of the matrix A, and the strictly upper */
/* >          triangular part of A is not referenced. */
/* >          On exit: */
/* >          if UPLO = 'U', the last NB columns have been reduced to */
/* >            tridiagonal form, with the diagonal elements overwriting */
/* >            the diagonal elements of A; the elements above the diagonal */
/* >            with the array TAU, represent the orthogonal matrix Q as a */
/* >            product of elementary reflectors; */
/* >          if UPLO = 'L', the first NB columns have been reduced to */
/* >            tridiagonal form, with the diagonal elements overwriting */
/* >            the diagonal elements of A; the elements below the diagonal */
/* >            with the array TAU, represent the  orthogonal matrix Q as a */
/* >            product of elementary reflectors. */
/* >          See Further Details. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= (1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] E */
/* > \verbatim */
/* >          E is DOUBLE PRECISION array, dimension (N-1) */
/* >          If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */
/* >          elements of the last NB columns of the reduced matrix; */
/* >          if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */
/* >          the first NB columns of the reduced matrix. */
/* > \endverbatim */
/* > */
/* > \param[out] TAU */
/* > \verbatim */
/* >          TAU is DOUBLE PRECISION array, dimension (N-1) */
/* >          The scalar factors of the elementary reflectors, stored in */
/* >          TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */
/* >          See Further Details. */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* >          W is DOUBLE PRECISION array, dimension (LDW,NB) */
/* >          The n-by-nb matrix W required to update the unreduced part */
/* >          of A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDW */
/* > \verbatim */
/* >          LDW is INTEGER */
/* >          The leading dimension of the array W. LDW >= f2cmax(1,N). */
/* > \endverbatim */

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

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

/* > \date December 2016 */

/* > \ingroup doubleOTHERauxiliary */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  If UPLO = 'U', the matrix Q is represented as a product of elementary */
/* >  reflectors */
/* > */
/* >     Q = H(n) H(n-1) . . . H(n-nb+1). */
/* > */
/* >  Each H(i) has the form */
/* > */
/* >     H(i) = I - tau * v * v**T */
/* > */
/* >  where tau is a real scalar, and v is a real vector with */
/* >  v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */
/* >  and tau in TAU(i-1). */
/* > */
/* >  If UPLO = 'L', the matrix Q is represented as a product of elementary */
/* >  reflectors */
/* > */
/* >     Q = H(1) H(2) . . . H(nb). */
/* > */
/* >  Each H(i) has the form */
/* > */
/* >     H(i) = I - tau * v * v**T */
/* > */
/* >  where tau is a real scalar, and v is a real vector with */
/* >  v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */
/* >  and tau in TAU(i). */
/* > */
/* >  The elements of the vectors v together form the n-by-nb matrix V */
/* >  which is needed, with W, to apply the transformation to the unreduced */
/* >  part of the matrix, using a symmetric rank-2k update of the form: */
/* >  A := A - V*W**T - W*V**T. */
/* > */
/* >  The contents of A on exit are illustrated by the following examples */
/* >  with n = 5 and nb = 2: */
/* > */
/* >  if UPLO = 'U':                       if UPLO = 'L': */
/* > */
/* >    (  a   a   a   v4  v5 )              (  d                  ) */
/* >    (      a   a   v4  v5 )              (  1   d              ) */
/* >    (          a   1   v5 )              (  v1  1   a          ) */
/* >    (              d   1  )              (  v1  v2  a   a      ) */
/* >    (                  d  )              (  v1  v2  a   a   a  ) */
/* > */
/* >  where d denotes a diagonal element of the reduced matrix, a denotes */
/* >  an element of the original matrix that is unchanged, and vi denotes */
/* >  an element of the vector defining H(i). */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ void dlatrd_(char *uplo, integer *n, integer *nb, doublereal *
	a, integer *lda, doublereal *e, doublereal *tau, doublereal *w, 
	integer *ldw)
{
    /* System generated locals */
    integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3;

    /* Local variables */
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    integer i__;
    doublereal alpha;
    extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ void dgemv_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *), daxpy_(integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *), 
	    dsymv_(char *, integer *, doublereal *, doublereal *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *), dlarfg_(integer *, doublereal *, doublereal *, integer *,
	     doublereal *);
    integer iw;


/*  -- LAPACK auxiliary 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 */


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


/*     Quick return if possible */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --e;
    --tau;
    w_dim1 = *ldw;
    w_offset = 1 + w_dim1 * 1;
    w -= w_offset;

    /* Function Body */
    if (*n <= 0) {
	return;
    }

    if (lsame_(uplo, "U")) {

/*        Reduce last NB columns of upper triangle */

	i__1 = *n - *nb + 1;
	for (i__ = *n; i__ >= i__1; --i__) {
	    iw = i__ - *n + *nb;
	    if (i__ < *n) {

/*              Update A(1:i,i) */

		i__2 = *n - i__;
		dgemv_("No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) * 
			a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, &
			c_b6, &a[i__ * a_dim1 + 1], &c__1);
		i__2 = *n - i__;
		dgemv_("No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) * 
			w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, &
			c_b6, &a[i__ * a_dim1 + 1], &c__1);
	    }
	    if (i__ > 1) {

/*              Generate elementary reflector H(i) to annihilate */
/*              A(1:i-2,i) */

		i__2 = i__ - 1;
		dlarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 + 
			1], &c__1, &tau[i__ - 1]);
		e[i__ - 1] = a[i__ - 1 + i__ * a_dim1];
		a[i__ - 1 + i__ * a_dim1] = 1.;

/*              Compute W(1:i-1,i) */

		i__2 = i__ - 1;
		dsymv_("Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ * 
			a_dim1 + 1], &c__1, &c_b16, &w[iw * w_dim1 + 1], &
			c__1);
		if (i__ < *n) {
		    i__2 = i__ - 1;
		    i__3 = *n - i__;
		    dgemv_("Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) * 
			    w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &c__1, &
			    c_b16, &w[i__ + 1 + iw * w_dim1], &c__1);
		    i__2 = i__ - 1;
		    i__3 = *n - i__;
		    dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) *
			     a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], &
			    c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1);
		    i__2 = i__ - 1;
		    i__3 = *n - i__;
		    dgemv_("Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) * 
			    a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], &c__1, &
			    c_b16, &w[i__ + 1 + iw * w_dim1], &c__1);
		    i__2 = i__ - 1;
		    i__3 = *n - i__;
		    dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) * 
			    w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], &
			    c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1);
		}
		i__2 = i__ - 1;
		dscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1);
		i__2 = i__ - 1;
		alpha = tau[i__ - 1] * -.5 * ddot_(&i__2, &w[iw * w_dim1 + 1],
			 &c__1, &a[i__ * a_dim1 + 1], &c__1);
		i__2 = i__ - 1;
		daxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * 
			w_dim1 + 1], &c__1);
	    }

/* L10: */
	}
    } else {

/*        Reduce first NB columns of lower triangle */

	i__1 = *nb;
	for (i__ = 1; i__ <= i__1; ++i__) {

/*           Update A(i:n,i) */

	    i__2 = *n - i__ + 1;
	    i__3 = i__ - 1;
	    dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda,
		     &w[i__ + w_dim1], ldw, &c_b6, &a[i__ + i__ * a_dim1], &
		    c__1);
	    i__2 = *n - i__ + 1;
	    i__3 = i__ - 1;
	    dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw,
		     &a[i__ + a_dim1], lda, &c_b6, &a[i__ + i__ * a_dim1], &
		    c__1);
	    if (i__ < *n) {

/*              Generate elementary reflector H(i) to annihilate */
/*              A(i+2:n,i) */

		i__2 = *n - i__;
/* Computing MIN */
		i__3 = i__ + 2;
		dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[f2cmin(i__3,*n) + 
			i__ * a_dim1], &c__1, &tau[i__]);
		e[i__] = a[i__ + 1 + i__ * a_dim1];
		a[i__ + 1 + i__ * a_dim1] = 1.;

/*              Compute W(i+1:n,i) */

		i__2 = *n - i__;
		dsymv_("Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1]
			, lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
			i__ + 1 + i__ * w_dim1], &c__1);
		i__2 = *n - i__;
		i__3 = i__ - 1;
		dgemv_("Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1],
			 ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
			i__ * w_dim1 + 1], &c__1);
		i__2 = *n - i__;
		i__3 = i__ - 1;
		dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + 
			a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[
			i__ + 1 + i__ * w_dim1], &c__1);
		i__2 = *n - i__;
		i__3 = i__ - 1;
		dgemv_("Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1],
			 lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
			i__ * w_dim1 + 1], &c__1);
		i__2 = *n - i__;
		i__3 = i__ - 1;
		dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 + 
			w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[
			i__ + 1 + i__ * w_dim1], &c__1);
		i__2 = *n - i__;
		dscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1);
		i__2 = *n - i__;
		alpha = tau[i__] * -.5 * ddot_(&i__2, &w[i__ + 1 + i__ * 
			w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1);
		i__2 = *n - i__;
		daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[
			i__ + 1 + i__ * w_dim1], &c__1);
	    }

/* L20: */
	}
    }

    return;

/*     End of DLATRD */

} /* dlatrd_ */