text: /* f2c.h  --  Standard Fortran to C header file */
  
  /**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
  
  	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
  
  #ifndef F2C_INCLUDE
  #define F2C_INCLUDE
  
  #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;
  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;}
  #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)); }
  #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  #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) = conj(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) (cimag(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;
  }
  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;
  }
  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;
  }
  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;
  	_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;
  }
  static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  	integer n = *n_, incx = *incx_, incy = *incy_, i;
  	_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;
  }	
  static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  	integer n = *n_, incx = *incx_, incy = *incy_, i;
  	_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;
  }
  static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  	integer n = *n_, incx = *incx_, incy = *incy_, i;
  	_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__1 = 1;
  static integer c_n1 = -1;
  static doublereal c_b12 = 1.;
  static doublereal c_b13 = 0.;
  static doublereal c_b21 = -1.;
  
  /* > \brief \b DSYTRF_AA_2STAGE */
  
  /*  =========== DOCUMENTATION =========== */
  
  /* Online html documentation available at */
  /*            http://www.netlib.org/lapack/explore-html/ */
  
  /* > \htmlonly */
  /* > Download DSYTRF_AA_2STAGE + dependencies */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrf_
  aa_2stage.f"> */
  /* > [TGZ]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrf_
  aa_2stage.f"> */
  /* > [ZIP]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrf_
  aa_2stage.f"> */
  /* > [TXT]</a> */
  /* > \endhtmlonly */
  
  /*  Definition: */
  /*  =========== */
  
  /*      SUBROUTINE DSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, */
  /*                                   IPIV2, WORK, LWORK, INFO ) */
  
  /*       CHARACTER          UPLO */
  /*       INTEGER            N, LDA, LTB, LWORK, INFO */
  /*       INTEGER            IPIV( * ), IPIV2( * ) */
  /*       DOUBLE PRECISION   A( LDA, * ), TB( * ), WORK( * ) */
  
  /* > \par Purpose: */
  /*  ============= */
  /* > */
  /* > \verbatim */
  /* > */
  /* > DSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A */
  /* > using the Aasen's algorithm.  The form of the factorization is */
  /* > */
  /* >    A = U**T*T*U  or  A = L*T*L**T */
  /* > */
  /* > where U (or L) is a product of permutation and unit upper (lower) */
  /* > triangular matrices, and T is a symmetric band matrix with the */
  /* > bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is */
  /* > LU factorized with partial pivoting). */
  /* > */
  /* > This is the blocked version of the algorithm, calling Level 3 BLAS. */
  /* > \endverbatim */
  
  /*  Arguments: */
  /*  ========== */
  
  /* > \param[in] UPLO */
  /* > \verbatim */
  /* >          UPLO is CHARACTER*1 */
  /* >          = 'U':  Upper triangle of A is stored; */
  /* >          = 'L':  Lower triangle of A is stored. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] N */
  /* > \verbatim */
  /* >          N is INTEGER */
  /* >          The order of the matrix A.  N >= 0. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,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, L is stored below (or above) the subdiaonal blocks, */
  /* >          when UPLO  is 'L' (or 'U'). */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LDA */
  /* > \verbatim */
  /* >          LDA is INTEGER */
  /* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
  /* > \endverbatim */
  /* > */
  /* > \param[out] TB */
  /* > \verbatim */
  /* >          TB is DOUBLE PRECISION array, dimension (LTB) */
  /* >          On exit, details of the LU factorization of the band matrix. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LTB */
  /* > \verbatim */
  /* >          LTB is INTEGER */
  /* >          The size of the array TB. LTB >= 4*N, internally */
  /* >          used to select NB such that LTB >= (3*NB+1)*N. */
  /* > */
  /* >          If LTB = -1, then a workspace query is assumed; the */
  /* >          routine only calculates the optimal size of LTB, */
  /* >          returns this value as the first entry of TB, and */
  /* >          no error message related to LTB is issued by XERBLA. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] IPIV */
  /* > \verbatim */
  /* >          IPIV is INTEGER array, dimension (N) */
  /* >          On exit, it contains the details of the interchanges, i.e., */
  /* >          the row and column k of A were interchanged with the */
  /* >          row and column IPIV(k). */
  /* > \endverbatim */
  /* > */
  /* > \param[out] IPIV2 */
  /* > \verbatim */
  /* >          IPIV2 is INTEGER array, dimension (N) */
  /* >          On exit, it contains the details of the interchanges, i.e., */
  /* >          the row and column k of T were interchanged with the */
  /* >          row and column IPIV2(k). */
  /* > \endverbatim */
  /* > */
  /* > \param[out] WORK */
  /* > \verbatim */
  /* >          WORK is DOUBLE PRECISION workspace of size LWORK */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LWORK */
  /* > \verbatim */
  /* >          LWORK is INTEGER */
  /* >          The size of WORK. LWORK >= N, internally used to select NB */
  /* >          such that LWORK >= N*NB. */
  /* > */
  /* >          If LWORK = -1, then a workspace query is assumed; the */
  /* >          routine only calculates the optimal size of the WORK array, */
  /* >          returns this value as the first entry of the WORK array, and */
  /* >          no error message related to LWORK is issued by XERBLA. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] INFO */
  /* > \verbatim */
  /* >          INFO is INTEGER */
  /* >          = 0:  successful exit */
  /* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
  /* >          > 0:  if INFO = i, band LU factorization failed on i-th column */
  /* > \endverbatim */
  
  /*  Authors: */
  /*  ======== */
  
  /* > \author Univ. of Tennessee */
  /* > \author Univ. of California Berkeley */
  /* > \author Univ. of Colorado Denver */
  /* > \author NAG Ltd. */
  
  /* > \date November 2017 */
  
  /* > \ingroup doubleSYcomputational */
  
  /*  ===================================================================== */
  /* Subroutine */ int dsytrf_aa_2stage_(char *uplo, integer *n, doublereal *a,
  	 integer *lda, doublereal *tb, integer *ltb, integer *ipiv, integer *
  	ipiv2, doublereal *work, integer *lwork, integer *info)
  {
      /* System generated locals */
      integer a_dim1, a_offset, i__1, i__2, i__3;
  
      /* Local variables */
      integer ldtb, i__, j, k;
      extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
  	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
  	    integer *, doublereal *, doublereal *, integer *);
      extern logical lsame_(char *, char *);
      integer iinfo;
      extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
  	    doublereal *, integer *), dswap_(integer *, doublereal *, integer 
  	    *, doublereal *, integer *), dtrsm_(char *, char *, char *, char *
  	    , integer *, integer *, doublereal *, doublereal *, integer *, 
  	    doublereal *, integer *);
      integer i1;
      logical upper;
      integer i2, jb, kb, nb, td, nt;
      extern /* Subroutine */ int dgbtrf_(integer *, integer *, integer *, 
  	    integer *, doublereal *, integer *, integer *, integer *), 
  	    dgetrf_(integer *, integer *, doublereal *, integer *, integer *, 
  	    integer *), dlacpy_(char *, integer *, integer *, doublereal *, 
  	    integer *, doublereal *, integer *), xerbla_(char *, 
  	    integer *, ftnlen);
      extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
  	    integer *, integer *, ftnlen, ftnlen);
      extern /* Subroutine */ int dlaset_(char *, integer *, integer *, 
  	    doublereal *, doublereal *, doublereal *, integer *), 
  	    dsygst_(integer *, char *, integer *, doublereal *, integer *, 
  	    doublereal *, integer *, integer *);
      logical tquery, wquery;
      doublereal piv;
  
  
  /*  -- LAPACK computational routine (version 3.8.0) -- */
  /*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
  /*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  /*     November 2017 */
  
  
  
  /*  ===================================================================== */
  
  
  /*     Test the input parameters. */
  
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1 * 1;
      a -= a_offset;
      --tb;
      --ipiv;
      --ipiv2;
      --work;
  
      /* Function Body */
      *info = 0;
      upper = lsame_(uplo, "U");
      wquery = *lwork == -1;
      tquery = *ltb == -1;
      if (! upper && ! lsame_(uplo, "L")) {
  	*info = -1;
      } else if (*n < 0) {
  	*info = -2;
      } else if (*lda < f2cmax(1,*n)) {
  	*info = -4;
      } else if (*ltb < *n << 2 && ! tquery) {
  	*info = -6;
      } else if (*lwork < *n && ! wquery) {
  	*info = -10;
      }
  
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("DSYTRF_AA_2STAGE", &i__1, (ftnlen)16);
  	return 0;
      }
  
  /*     Answer the query */
  
      nb = ilaenv_(&c__1, "DSYTRF_AA_2STAGE", uplo, n, &c_n1, &c_n1, &c_n1, (
  	    ftnlen)16, (ftnlen)1);
      if (*info == 0) {
  	if (tquery) {
  	    tb[1] = (doublereal) ((nb * 3 + 1) * *n);
  	}
  	if (wquery) {
  	    work[1] = (doublereal) (*n * nb);
  	}
      }
      if (tquery || wquery) {
  	return 0;
      }
  
  /*     Quick return */
  
      if (*n == 0) {
  	return 0;
      }
  
  /*     Determine the number of the block size */
  
      ldtb = *ltb / *n;
      if (ldtb < nb * 3 + 1) {
  	nb = (ldtb - 1) / 3;
      }
      if (*lwork < nb * *n) {
  	nb = *lwork / *n;
      }
  
  /*     Determine the number of the block columns */
  
      nt = (*n + nb - 1) / nb;
      td = nb << 1;
      kb = f2cmin(nb,*n);
  
  /*     Initialize vectors/matrices */
  
      i__1 = kb;
      for (j = 1; j <= i__1; ++j) {
  	ipiv[j] = j;
      }
  
  /*     Save NB */
  
      tb[1] = (doublereal) nb;
  
      if (upper) {
  
  /*        ..................................................... */
  /*        Factorize A as U**T*D*U using the upper triangle of A */
  /*        ..................................................... */
  
  	i__1 = nt - 1;
  	for (j = 0; j <= i__1; ++j) {
  
  /*           Generate Jth column of W and H */
  
  /* Computing MIN */
  	    i__2 = nb, i__3 = *n - j * nb;
  	    kb = f2cmin(i__2,i__3);
  	    i__2 = j - 1;
  	    for (i__ = 1; i__ <= i__2; ++i__) {
  		if (i__ == 1) {
  /*                 H(I,J) = T(I,I)*U(I,J) + T(I,I+1)*U(I+1,J) */
  		    if (i__ == j - 1) {
  			jb = nb + kb;
  		    } else {
  			jb = nb << 1;
  		    }
  		    i__3 = ldtb - 1;
  		    dgemm_("NoTranspose", "NoTranspose", &nb, &kb, &jb, &
  			    c_b12, &tb[td + 1 + i__ * nb * ldtb], &i__3, &a[(
  			    i__ - 1) * nb + 1 + (j * nb + 1) * a_dim1], lda, &
  			    c_b13, &work[i__ * nb + 1], n);
  		} else {
  /*                 H(I,J) = T(I,I-1)*U(I-1,J) + T(I,I)*U(I,J) + T(I,I+1)*U(I+1,J) */
  		    if (i__ == j - 1) {
  			jb = (nb << 1) + kb;
  		    } else {
  			jb = nb * 3;
  		    }
  		    i__3 = ldtb - 1;
  		    dgemm_("NoTranspose", "NoTranspose", &nb, &kb, &jb, &
  			    c_b12, &tb[td + nb + 1 + (i__ - 1) * nb * ldtb], &
  			    i__3, &a[(i__ - 2) * nb + 1 + (j * nb + 1) * 
  			    a_dim1], lda, &c_b13, &work[i__ * nb + 1], n);
  		}
  	    }
  
  /*           Compute T(J,J) */
  
  	    i__2 = ldtb - 1;
  	    dlacpy_("Upper", &kb, &kb, &a[j * nb + 1 + (j * nb + 1) * a_dim1],
  		     lda, &tb[td + 1 + j * nb * ldtb], &i__2);
  	    if (j > 1) {
  /*              T(J,J) = U(1:J,J)'*H(1:J) */
  		i__2 = (j - 1) * nb;
  		i__3 = ldtb - 1;
  		dgemm_("Transpose", "NoTranspose", &kb, &kb, &i__2, &c_b21, &
  			a[(j * nb + 1) * a_dim1 + 1], lda, &work[nb + 1], n, &
  			c_b12, &tb[td + 1 + j * nb * ldtb], &i__3);
  /*              T(J,J) += U(J,J)'*T(J,J-1)*U(J-1,J) */
  		i__2 = ldtb - 1;
  		dgemm_("Transpose", "NoTranspose", &kb, &nb, &kb, &c_b12, &a[(
  			j - 1) * nb + 1 + (j * nb + 1) * a_dim1], lda, &tb[td 
  			+ nb + 1 + (j - 1) * nb * ldtb], &i__2, &c_b13, &work[
  			1], n);
  		i__2 = ldtb - 1;
  		dgemm_("NoTranspose", "NoTranspose", &kb, &kb, &nb, &c_b21, &
  			work[1], n, &a[(j - 2) * nb + 1 + (j * nb + 1) * 
  			a_dim1], lda, &c_b12, &tb[td + 1 + j * nb * ldtb], &
  			i__2);
  	    }
  	    if (j > 0) {
  		i__2 = ldtb - 1;
  		dsygst_(&c__1, "Upper", &kb, &tb[td + 1 + j * nb * ldtb], &
  			i__2, &a[(j - 1) * nb + 1 + (j * nb + 1) * a_dim1], 
  			lda, &iinfo);
  	    }
  
  /*           Expand T(J,J) into full format */
  
  	    i__2 = kb;
  	    for (i__ = 1; i__ <= i__2; ++i__) {
  		i__3 = kb;
  		for (k = i__ + 1; k <= i__3; ++k) {
  		    tb[td + (k - i__) + 1 + (j * nb + i__ - 1) * ldtb] = tb[
  			    td - (k - (i__ + 1)) + (j * nb + k - 1) * ldtb];
  		}
  	    }
  
  	    if (j < nt - 1) {
  		if (j > 0) {
  
  /*                 Compute H(J,J) */
  
  		    if (j == 1) {
  			i__2 = ldtb - 1;
  			dgemm_("NoTranspose", "NoTranspose", &kb, &kb, &kb, &
  				c_b12, &tb[td + 1 + j * nb * ldtb], &i__2, &a[
  				(j - 1) * nb + 1 + (j * nb + 1) * a_dim1], 
  				lda, &c_b13, &work[j * nb + 1], n);
  		    } else {
  			i__2 = nb + kb;
  			i__3 = ldtb - 1;
  			dgemm_("NoTranspose", "NoTranspose", &kb, &kb, &i__2, 
  				&c_b12, &tb[td + nb + 1 + (j - 1) * nb * ldtb]
  				, &i__3, &a[(j - 2) * nb + 1 + (j * nb + 1) * 
  				a_dim1], lda, &c_b13, &work[j * nb + 1], n);
  		    }
  
  /*                 Update with the previous column */
  
  		    i__2 = *n - (j + 1) * nb;
  		    i__3 = j * nb;
  		    dgemm_("Transpose", "NoTranspose", &nb, &i__2, &i__3, &
  			    c_b21, &work[nb + 1], n, &a[((j + 1) * nb + 1) * 
  			    a_dim1 + 1], lda, &c_b12, &a[j * nb + 1 + ((j + 1)
  			     * nb + 1) * a_dim1], lda);
  		}
  
  /*              Copy panel to workspace to call DGETRF */
  
  		i__2 = nb;
  		for (k = 1; k <= i__2; ++k) {
  		    i__3 = *n - (j + 1) * nb;
  		    dcopy_(&i__3, &a[j * nb + k + ((j + 1) * nb + 1) * a_dim1]
  			    , lda, &work[(k - 1) * *n + 1], &c__1);
  		}
  
  /*              Factorize panel */
  
  		i__2 = *n - (j + 1) * nb;
  		dgetrf_(&i__2, &nb, &work[1], n, &ipiv[(j + 1) * nb + 1], &
  			iinfo);
  /*               IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN */
  /*                  INFO = IINFO+(J+1)*NB */
  /*               END IF */
  
  /*              Copy panel back */
  
  		i__2 = nb;
  		for (k = 1; k <= i__2; ++k) {
  		    i__3 = *n - (j + 1) * nb;
  		    dcopy_(&i__3, &work[(k - 1) * *n + 1], &c__1, &a[j * nb + 
  			    k + ((j + 1) * nb + 1) * a_dim1], lda);
  		}
  
  /*              Compute T(J+1, J), zero out for GEMM update */
  
  /* Computing MIN */
  		i__2 = nb, i__3 = *n - (j + 1) * nb;
  		kb = f2cmin(i__2,i__3);
  		i__2 = ldtb - 1;
  		dlaset_("Full", &kb, &nb, &c_b13, &c_b13, &tb[td + nb + 1 + j 
  			* nb * ldtb], &i__2);
  		i__2 = ldtb - 1;
  		dlacpy_("Upper", &kb, &nb, &work[1], n, &tb[td + nb + 1 + j * 
  			nb * ldtb], &i__2);
  		if (j > 0) {
  		    i__2 = ldtb - 1;
  		    dtrsm_("R", "U", "N", "U", &kb, &nb, &c_b12, &a[(j - 1) * 
  			    nb + 1 + (j * nb + 1) * a_dim1], lda, &tb[td + nb 
  			    + 1 + j * nb * ldtb], &i__2);
  		}
  
  /*              Copy T(J,J+1) into T(J+1, J), both upper/lower for GEMM */
  /*              updates */
  
  		i__2 = nb;
  		for (k = 1; k <= i__2; ++k) {
  		    i__3 = kb;
  		    for (i__ = 1; i__ <= i__3; ++i__) {
  			tb[td - nb + k - i__ + 1 + (j * nb + nb + i__ - 1) * 
  				ldtb] = tb[td + nb + i__ - k + 1 + (j * nb + 
  				k - 1) * ldtb];
  		    }
  		}
  		dlaset_("Lower", &kb, &nb, &c_b13, &c_b12, &a[j * nb + 1 + ((
  			j + 1) * nb + 1) * a_dim1], lda);
  
  /*              Apply pivots to trailing submatrix of A */
  
  		i__2 = kb;
  		for (k = 1; k <= i__2; ++k) {
  /*                 > Adjust ipiv */
  		    ipiv[(j + 1) * nb + k] += (j + 1) * nb;
  
  		    i1 = (j + 1) * nb + k;
  		    i2 = ipiv[(j + 1) * nb + k];
  		    if (i1 != i2) {
  /*                    > Apply pivots to previous columns of L */
  			i__3 = k - 1;
  			dswap_(&i__3, &a[(j + 1) * nb + 1 + i1 * a_dim1], &
  				c__1, &a[(j + 1) * nb + 1 + i2 * a_dim1], &
  				c__1);
  /*                    > Swap A(I1+1:M, I1) with A(I2, I1+1:M) */
  			if (i2 > i1 + 1) {
  			    i__3 = i2 - i1 - 1;
  			    dswap_(&i__3, &a[i1 + (i1 + 1) * a_dim1], lda, &a[
  				    i1 + 1 + i2 * a_dim1], &c__1);
  			}
  /*                    > Swap A(I2+1:M, I1) with A(I2+1:M, I2) */
  			if (i2 < *n) {
  			    i__3 = *n - i2;
  			    dswap_(&i__3, &a[i1 + (i2 + 1) * a_dim1], lda, &a[
  				    i2 + (i2 + 1) * a_dim1], lda);
  			}
  /*                    > Swap A(I1, I1) with A(I2, I2) */
  			piv = a[i1 + i1 * a_dim1];
  			a[i1 + i1 * a_dim1] = a[i2 + i2 * a_dim1];
  			a[i2 + i2 * a_dim1] = piv;
  /*                    > Apply pivots to previous columns of L */
  			if (j > 0) {
  			    i__3 = j * nb;
  			    dswap_(&i__3, &a[i1 * a_dim1 + 1], &c__1, &a[i2 * 
  				    a_dim1 + 1], &c__1);
  			}
  		    }
  		}
  	    }
  	}
      } else {
  
  /*        ..................................................... */
  /*        Factorize A as L*D*L**T using the lower triangle of A */
  /*        ..................................................... */
  
  	i__1 = nt - 1;
  	for (j = 0; j <= i__1; ++j) {
  
  /*           Generate Jth column of W and H */
  
  /* Computing MIN */
  	    i__2 = nb, i__3 = *n - j * nb;
  	    kb = f2cmin(i__2,i__3);
  	    i__2 = j - 1;
  	    for (i__ = 1; i__ <= i__2; ++i__) {
  		if (i__ == 1) {
  /*                  H(I,J) = T(I,I)*L(J,I)' + T(I+1,I)'*L(J,I+1)' */
  		    if (i__ == j - 1) {
  			jb = nb + kb;
  		    } else {
  			jb = nb << 1;
  		    }
  		    i__3 = ldtb - 1;
  		    dgemm_("NoTranspose", "Transpose", &nb, &kb, &jb, &c_b12, 
  			    &tb[td + 1 + i__ * nb * ldtb], &i__3, &a[j * nb + 
  			    1 + ((i__ - 1) * nb + 1) * a_dim1], lda, &c_b13, &
  			    work[i__ * nb + 1], n);
  		} else {
  /*                 H(I,J) = T(I,I-1)*L(J,I-1)' + T(I,I)*L(J,I)' + T(I,I+1)*L(J,I+1)' */
  		    if (i__ == j - 1) {
  			jb = (nb << 1) + kb;
  		    } else {
  			jb = nb * 3;
  		    }
  		    i__3 = ldtb - 1;
  		    dgemm_("NoTranspose", "Transpose", &nb, &kb, &jb, &c_b12, 
  			    &tb[td + nb + 1 + (i__ - 1) * nb * ldtb], &i__3, &
  			    a[j * nb + 1 + ((i__ - 2) * nb + 1) * a_dim1], 
  			    lda, &c_b13, &work[i__ * nb + 1], n);
  		}
  	    }
  
  /*           Compute T(J,J) */
  
  	    i__2 = ldtb - 1;
  	    dlacpy_("Lower", &kb, &kb, &a[j * nb + 1 + (j * nb + 1) * a_dim1],
  		     lda, &tb[td + 1 + j * nb * ldtb], &i__2);
  	    if (j > 1) {
  /*              T(J,J) = L(J,1:J)*H(1:J) */
  		i__2 = (j - 1) * nb;
  		i__3 = ldtb - 1;
  		dgemm_("NoTranspose", "NoTranspose", &kb, &kb, &i__2, &c_b21, 
  			&a[j * nb + 1 + a_dim1], lda, &work[nb + 1], n, &
  			c_b12, &tb[td + 1 + j * nb * ldtb], &i__3);
  /*              T(J,J) += L(J,J)*T(J,J-1)*L(J,J-1)' */
  		i__2 = ldtb - 1;
  		dgemm_("NoTranspose", "NoTranspose", &kb, &nb, &kb, &c_b12, &
  			a[j * nb + 1 + ((j - 1) * nb + 1) * a_dim1], lda, &tb[
  			td + nb + 1 + (j - 1) * nb * ldtb], &i__2, &c_b13, &
  			work[1], n);
  		i__2 = ldtb - 1;
  		dgemm_("NoTranspose", "Transpose", &kb, &kb, &nb, &c_b21, &
  			work[1], n, &a[j * nb + 1 + ((j - 2) * nb + 1) * 
  			a_dim1], lda, &c_b12, &tb[td + 1 + j * nb * ldtb], &
  			i__2);
  	    }
  	    if (j > 0) {
  		i__2 = ldtb - 1;
  		dsygst_(&c__1, "Lower", &kb, &tb[td + 1 + j * nb * ldtb], &
  			i__2, &a[j * nb + 1 + ((j - 1) * nb + 1) * a_dim1], 
  			lda, &iinfo);
  	    }
  
  /*           Expand T(J,J) into full format */
  
  	    i__2 = kb;
  	    for (i__ = 1; i__ <= i__2; ++i__) {
  		i__3 = kb;
  		for (k = i__ + 1; k <= i__3; ++k) {
  		    tb[td - (k - (i__ + 1)) + (j * nb + k - 1) * ldtb] = tb[
  			    td + (k - i__) + 1 + (j * nb + i__ - 1) * ldtb];
  		}
  	    }
  
  	    if (j < nt - 1) {
  		if (j > 0) {
  
  /*                 Compute H(J,J) */
  
  		    if (j == 1) {
  			i__2 = ldtb - 1;
  			dgemm_("NoTranspose", "Transpose", &kb, &kb, &kb, &
  				c_b12, &tb[td + 1 + j * nb * ldtb], &i__2, &a[
  				j * nb + 1 + ((j - 1) * nb + 1) * a_dim1], 
  				lda, &c_b13, &work[j * nb + 1], n);
  		    } else {
  			i__2 = nb + kb;
  			i__3 = ldtb - 1;
  			dgemm_("NoTranspose", "Transpose", &kb, &kb, &i__2, &
  				c_b12, &tb[td + nb + 1 + (j - 1) * nb * ldtb],
  				 &i__3, &a[j * nb + 1 + ((j - 2) * nb + 1) * 
  				a_dim1], lda, &c_b13, &work[j * nb + 1], n);
  		    }
  
  /*                 Update with the previous column */
  
  		    i__2 = *n - (j + 1) * nb;
  		    i__3 = j * nb;
  		    dgemm_("NoTranspose", "NoTranspose", &i__2, &nb, &i__3, &
  			    c_b21, &a[(j + 1) * nb + 1 + a_dim1], lda, &work[
  			    nb + 1], n, &c_b12, &a[(j + 1) * nb + 1 + (j * nb 
  			    + 1) * a_dim1], lda);
  		}
  
  /*              Factorize panel */
  
  		i__2 = *n - (j + 1) * nb;
  		dgetrf_(&i__2, &nb, &a[(j + 1) * nb + 1 + (j * nb + 1) * 
  			a_dim1], lda, &ipiv[(j + 1) * nb + 1], &iinfo);
  /*               IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN */
  /*                  INFO = IINFO+(J+1)*NB */
  /*               END IF */
  
  /*              Compute T(J+1, J), zero out for GEMM update */
  
  /* Computing MIN */
  		i__2 = nb, i__3 = *n - (j + 1) * nb;
  		kb = f2cmin(i__2,i__3);
  		i__2 = ldtb - 1;
  		dlaset_("Full", &kb, &nb, &c_b13, &c_b13, &tb[td + nb + 1 + j 
  			* nb * ldtb], &i__2);
  		i__2 = ldtb - 1;
  		dlacpy_("Upper", &kb, &nb, &a[(j + 1) * nb + 1 + (j * nb + 1) 
  			* a_dim1], lda, &tb[td + nb + 1 + j * nb * ldtb], &
  			i__2);
  		if (j > 0) {
  		    i__2 = ldtb - 1;
  		    dtrsm_("R", "L", "T", "U", &kb, &nb, &c_b12, &a[j * nb + 
  			    1 + ((j - 1) * nb + 1) * a_dim1], lda, &tb[td + 
  			    nb + 1 + j * nb * ldtb], &i__2);
  		}
  
  /*              Copy T(J+1,J) into T(J, J+1), both upper/lower for GEMM */
  /*              updates */
  
  		i__2 = nb;
  		for (k = 1; k <= i__2; ++k) {
  		    i__3 = kb;
  		    for (i__ = 1; i__ <= i__3; ++i__) {
  			tb[td - nb + k - i__ + 1 + (j * nb + nb + i__ - 1) * 
  				ldtb] = tb[td + nb + i__ - k + 1 + (j * nb + 
  				k - 1) * ldtb];
  		    }
  		}
  		dlaset_("Upper", &kb, &nb, &c_b13, &c_b12, &a[(j + 1) * nb + 
  			1 + (j * nb + 1) * a_dim1], lda);
  
  /*              Apply pivots to trailing submatrix of A */
  
  		i__2 = kb;
  		for (k = 1; k <= i__2; ++k) {
  /*                 > Adjust ipiv */
  		    ipiv[(j + 1) * nb + k] += (j + 1) * nb;
  
  		    i1 = (j + 1) * nb + k;
  		    i2 = ipiv[(j + 1) * nb + k];
  		    if (i1 != i2) {
  /*                    > Apply pivots to previous columns of L */
  			i__3 = k - 1;
  			dswap_(&i__3, &a[i1 + ((j + 1) * nb + 1) * a_dim1], 
  				lda, &a[i2 + ((j + 1) * nb + 1) * a_dim1], 
  				lda);
  /*                    > Swap A(I1+1:M, I1) with A(I2, I1+1:M) */
  			if (i2 > i1 + 1) {
  			    i__3 = i2 - i1 - 1;
  			    dswap_(&i__3, &a[i1 + 1 + i1 * a_dim1], &c__1, &a[
  				    i2 + (i1 + 1) * a_dim1], lda);
  			}
  /*                    > Swap A(I2+1:M, I1) with A(I2+1:M, I2) */
  			if (i2 < *n) {
  			    i__3 = *n - i2;
  			    dswap_(&i__3, &a[i2 + 1 + i1 * a_dim1], &c__1, &a[
  				    i2 + 1 + i2 * a_dim1], &c__1);
  			}
  /*                    > Swap A(I1, I1) with A(I2, I2) */
  			piv = a[i1 + i1 * a_dim1];
  			a[i1 + i1 * a_dim1] = a[i2 + i2 * a_dim1];
  			a[i2 + i2 * a_dim1] = piv;
  /*                    > Apply pivots to previous columns of L */
  			if (j > 0) {
  			    i__3 = j * nb;
  			    dswap_(&i__3, &a[i1 + a_dim1], lda, &a[i2 + 
  				    a_dim1], lda);
  			}
  		    }
  		}
  
  /*              Apply pivots to previous columns of L */
  
  /*               CALL DLASWP( J*NB, A( 1, 1 ), LDA, */
  /*     $                     (J+1)*NB+1, (J+1)*NB+KB, IPIV, 1 ) */
  	    }
  	}
      }
  
  /*     Factor the band matrix */
      dgbtrf_(n, n, &nb, &nb, &tb[1], &ldtb, &ipiv2[1], info);
  
      return 0;
  
  /*     End of DSYTRF_AA_2STAGE */
  
  } /* dsytrf_aa_2stage__ */
  
  