#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 real c_b12 = 1.f;
static real c_b15 = -1.f;

/* > \brief \b SPFTRF */

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

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

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

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

/*       SUBROUTINE SPFTRF( TRANSR, UPLO, N, A, INFO ) */

/*       CHARACTER          TRANSR, UPLO */
/*       INTEGER            N, INFO */
/*       REAL               A( 0: * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SPFTRF computes the Cholesky factorization of a real symmetric */
/* > positive definite matrix A. */
/* > */
/* > The factorization has the form */
/* >    A = U**T * U,  if UPLO = 'U', or */
/* >    A = L  * L**T,  if UPLO = 'L', */
/* > where U is an upper triangular matrix and L is lower triangular. */
/* > */
/* > This is the block version of the algorithm, calling Level 3 BLAS. */
/* > \endverbatim */

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

/* > \param[in] TRANSR */
/* > \verbatim */
/* >          TRANSR is CHARACTER*1 */
/* >          = 'N':  The Normal TRANSR of RFP A is stored; */
/* >          = 'T':  The Transpose TRANSR of RFP A is stored. */
/* > \endverbatim */
/* > */
/* > \param[in] UPLO */
/* > \verbatim */
/* >          UPLO is CHARACTER*1 */
/* >          = 'U':  Upper triangle of RFP A is stored; */
/* >          = 'L':  Lower triangle of RFP 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 REAL array, dimension ( N*(N+1)/2 ); */
/* >          On entry, the symmetric matrix A in RFP format. RFP format is */
/* >          described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' */
/* >          then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is */
/* >          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is */
/* >          the transpose of RFP A as defined when */
/* >          TRANSR = 'N'. The contents of RFP A are defined by UPLO as */
/* >          follows: If UPLO = 'U' the RFP A contains the NT elements of */
/* >          upper packed A. If UPLO = 'L' the RFP A contains the elements */
/* >          of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = */
/* >          'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N */
/* >          is odd. See the Note below for more details. */
/* > */
/* >          On exit, if INFO = 0, the factor U or L from the Cholesky */
/* >          factorization RFP A = U**T*U or RFP A = L*L**T. */
/* > \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, the leading minor of order i is not */
/* >                positive definite, and the factorization could not be */
/* >                completed. */
/* > \endverbatim */

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

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

/* > \date December 2016 */

/* > \ingroup realOTHERcomputational */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  We first consider Rectangular Full Packed (RFP) Format when N is */
/* >  even. We give an example where N = 6. */
/* > */
/* >      AP is Upper             AP is Lower */
/* > */
/* >   00 01 02 03 04 05       00 */
/* >      11 12 13 14 15       10 11 */
/* >         22 23 24 25       20 21 22 */
/* >            33 34 35       30 31 32 33 */
/* >               44 45       40 41 42 43 44 */
/* >                  55       50 51 52 53 54 55 */
/* > */
/* > */
/* >  Let TRANSR = 'N'. RFP holds AP as follows: */
/* >  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */
/* >  three columns of AP upper. The lower triangle A(4:6,0:2) consists of */
/* >  the transpose of the first three columns of AP upper. */
/* >  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */
/* >  three columns of AP lower. The upper triangle A(0:2,0:2) consists of */
/* >  the transpose of the last three columns of AP lower. */
/* >  This covers the case N even and TRANSR = 'N'. */
/* > */
/* >         RFP A                   RFP A */
/* > */
/* >        03 04 05                33 43 53 */
/* >        13 14 15                00 44 54 */
/* >        23 24 25                10 11 55 */
/* >        33 34 35                20 21 22 */
/* >        00 44 45                30 31 32 */
/* >        01 11 55                40 41 42 */
/* >        02 12 22                50 51 52 */
/* > */
/* >  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */
/* >  transpose of RFP A above. One therefore gets: */
/* > */
/* > */
/* >           RFP A                   RFP A */
/* > */
/* >     03 13 23 33 00 01 02    33 00 10 20 30 40 50 */
/* >     04 14 24 34 44 11 12    43 44 11 21 31 41 51 */
/* >     05 15 25 35 45 55 22    53 54 55 22 32 42 52 */
/* > */
/* > */
/* >  We then consider Rectangular Full Packed (RFP) Format when N is */
/* >  odd. We give an example where N = 5. */
/* > */
/* >     AP is Upper                 AP is Lower */
/* > */
/* >   00 01 02 03 04              00 */
/* >      11 12 13 14              10 11 */
/* >         22 23 24              20 21 22 */
/* >            33 34              30 31 32 33 */
/* >               44              40 41 42 43 44 */
/* > */
/* > */
/* >  Let TRANSR = 'N'. RFP holds AP as follows: */
/* >  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */
/* >  three columns of AP upper. The lower triangle A(3:4,0:1) consists of */
/* >  the transpose of the first two columns of AP upper. */
/* >  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */
/* >  three columns of AP lower. The upper triangle A(0:1,1:2) consists of */
/* >  the transpose of the last two columns of AP lower. */
/* >  This covers the case N odd and TRANSR = 'N'. */
/* > */
/* >         RFP A                   RFP A */
/* > */
/* >        02 03 04                00 33 43 */
/* >        12 13 14                10 11 44 */
/* >        22 23 24                20 21 22 */
/* >        00 33 34                30 31 32 */
/* >        01 11 44                40 41 42 */
/* > */
/* >  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */
/* >  transpose of RFP A above. One therefore gets: */
/* > */
/* >           RFP A                   RFP A */
/* > */
/* >     02 12 22 00 01             00 10 20 30 40 50 */
/* >     03 13 23 33 11             33 11 21 31 41 51 */
/* >     04 14 24 34 44             43 44 22 32 42 52 */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ void spftrf_(char *transr, char *uplo, integer *n, real *a, 
	integer *info)
{
    /* System generated locals */
    integer i__1, i__2;

    /* Local variables */
    integer k;
    logical normaltransr;
    extern logical lsame_(char *, char *);
    logical lower;
    integer n1, n2;
    extern /* Subroutine */ void strsm_(char *, char *, char *, char *, 
	    integer *, integer *, real *, real *, integer *, real *, integer *
	    ), ssyrk_(char *, char *, integer 
	    *, integer *, real *, real *, integer *, real *, real *, integer *
	    );
    extern int xerbla_(char *, integer *, ftnlen);
    logical nisodd;
    extern /* Subroutine */ int spotrf_(char *, integer *, real *, integer *, 
	    integer *);


/*  -- 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. */

    *info = 0;
    normaltransr = lsame_(transr, "N");
    lower = lsame_(uplo, "L");
    if (! normaltransr && ! lsame_(transr, "T")) {
	*info = -1;
    } else if (! lower && ! lsame_(uplo, "U")) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SPFTRF", &i__1, (ftnlen)6);
	return;
    }

/*     Quick return if possible */

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

/*     If N is odd, set NISODD = .TRUE. */
/*     If N is even, set K = N/2 and NISODD = .FALSE. */

    if (*n % 2 == 0) {
	k = *n / 2;
	nisodd = FALSE_;
    } else {
	nisodd = TRUE_;
    }

/*     Set N1 and N2 depending on LOWER */

    if (lower) {
	n2 = *n / 2;
	n1 = *n - n2;
    } else {
	n1 = *n / 2;
	n2 = *n - n1;
    }

/*     start execution: there are eight cases */

    if (nisodd) {

/*        N is odd */

	if (normaltransr) {

/*           N is odd and TRANSR = 'N' */

	    if (lower) {

/*             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) ) */
/*             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0) */
/*             T1 -> a(0), T2 -> a(n), S -> a(n1) */

		spotrf_("L", &n1, a, n, info);
		if (*info > 0) {
		    return;
		}
		strsm_("R", "L", "T", "N", &n2, &n1, &c_b12, a, n, &a[n1], n);
		ssyrk_("U", "N", &n2, &n1, &c_b15, &a[n1], n, &c_b12, &a[*n], 
			n);
		spotrf_("U", &n2, &a[*n], n, info);
		if (*info > 0) {
		    *info += n1;
		}

	    } else {

/*             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1) */
/*             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0) */
/*             T1 -> a(n2), T2 -> a(n1), S -> a(0) */

		spotrf_("L", &n1, &a[n2], n, info);
		if (*info > 0) {
		    return;
		}
		strsm_("L", "L", "N", "N", &n1, &n2, &c_b12, &a[n2], n, a, n);
		ssyrk_("U", "T", &n2, &n1, &c_b15, a, n, &c_b12, &a[n1], n);
		spotrf_("U", &n2, &a[n1], n, info);
		if (*info > 0) {
		    *info += n1;
		}

	    }

	} else {

/*           N is odd and TRANSR = 'T' */

	    if (lower) {

/*              SRPA for LOWER, TRANSPOSE and N is odd */
/*              T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1) */
/*              T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1 */

		spotrf_("U", &n1, a, &n1, info);
		if (*info > 0) {
		    return;
		}
		strsm_("L", "U", "T", "N", &n1, &n2, &c_b12, a, &n1, &a[n1 * 
			n1], &n1);
		ssyrk_("L", "T", &n2, &n1, &c_b15, &a[n1 * n1], &n1, &c_b12, &
			a[1], &n1);
		spotrf_("L", &n2, &a[1], &n1, info);
		if (*info > 0) {
		    *info += n1;
		}

	    } else {

/*              SRPA for UPPER, TRANSPOSE and N is odd */
/*              T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0) */
/*              T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2 */

		spotrf_("U", &n1, &a[n2 * n2], &n2, info);
		if (*info > 0) {
		    return;
		}
		strsm_("R", "U", "N", "N", &n2, &n1, &c_b12, &a[n2 * n2], &n2,
			 a, &n2);
		ssyrk_("L", "N", &n2, &n1, &c_b15, a, &n2, &c_b12, &a[n1 * n2]
			, &n2);
		spotrf_("L", &n2, &a[n1 * n2], &n2, info);
		if (*info > 0) {
		    *info += n1;
		}

	    }

	}

    } else {

/*        N is even */

	if (normaltransr) {

/*           N is even and TRANSR = 'N' */

	    if (lower) {

/*              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) ) */
/*              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0) */
/*              T1 -> a(1), T2 -> a(0), S -> a(k+1) */

		i__1 = *n + 1;
		spotrf_("L", &k, &a[1], &i__1, info);
		if (*info > 0) {
		    return;
		}
		i__1 = *n + 1;
		i__2 = *n + 1;
		strsm_("R", "L", "T", "N", &k, &k, &c_b12, &a[1], &i__1, &a[k 
			+ 1], &i__2);
		i__1 = *n + 1;
		i__2 = *n + 1;
		ssyrk_("U", "N", &k, &k, &c_b15, &a[k + 1], &i__1, &c_b12, a, 
			&i__2);
		i__1 = *n + 1;
		spotrf_("U", &k, a, &i__1, info);
		if (*info > 0) {
		    *info += k;
		}

	    } else {

/*              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) ) */
/*              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0) */
/*              T1 -> a(k+1), T2 -> a(k), S -> a(0) */

		i__1 = *n + 1;
		spotrf_("L", &k, &a[k + 1], &i__1, info);
		if (*info > 0) {
		    return;
		}
		i__1 = *n + 1;
		i__2 = *n + 1;
		strsm_("L", "L", "N", "N", &k, &k, &c_b12, &a[k + 1], &i__1, 
			a, &i__2);
		i__1 = *n + 1;
		i__2 = *n + 1;
		ssyrk_("U", "T", &k, &k, &c_b15, a, &i__1, &c_b12, &a[k], &
			i__2);
		i__1 = *n + 1;
		spotrf_("U", &k, &a[k], &i__1, info);
		if (*info > 0) {
		    *info += k;
		}

	    }

	} else {

/*           N is even and TRANSR = 'T' */

	    if (lower) {

/*              SRPA for LOWER, TRANSPOSE and N is even (see paper) */
/*              T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1) */
/*              T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k */

		spotrf_("U", &k, &a[k], &k, info);
		if (*info > 0) {
		    return;
		}
		strsm_("L", "U", "T", "N", &k, &k, &c_b12, &a[k], &n1, &a[k * 
			(k + 1)], &k);
		ssyrk_("L", "T", &k, &k, &c_b15, &a[k * (k + 1)], &k, &c_b12, 
			a, &k);
		spotrf_("L", &k, a, &k, info);
		if (*info > 0) {
		    *info += k;
		}

	    } else {

/*              SRPA for UPPER, TRANSPOSE and N is even (see paper) */
/*              T1 -> B(0,k+1),     T2 -> B(0,k),   S -> B(0,0) */
/*              T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k */

		spotrf_("U", &k, &a[k * (k + 1)], &k, info);
		if (*info > 0) {
		    return;
		}
		strsm_("R", "U", "N", "N", &k, &k, &c_b12, &a[k * (k + 1)], &
			k, a, &k);
		ssyrk_("L", "N", &k, &k, &c_b15, a, &k, &c_b12, &a[k * k], &k);
		spotrf_("L", &k, &a[k * k], &k, info);
		if (*info > 0) {
		    *info += k;
		}

	    }

	}

    }

    return;

/*     End of SPFTRF */

} /* spftrf_ */

