OpenBLAS/lapack-netlib/SRC/clahef_aa.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 complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__1 = 1;

/* > \brief \b CLAHEF_AA */

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

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

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

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

/*       SUBROUTINE CLAHEF_AA( UPLO, J1, M, NB, A, LDA, IPIV, */
/*                             H, LDH, WORK ) */

/*       CHARACTER    UPLO */
/*       INTEGER      J1, M, NB, LDA, LDH */
/*       INTEGER      IPIV( * ) */
/*       COMPLEX      A( LDA, * ), H( LDH, * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > CLAHEF_AA factorizes a panel of a complex hermitian matrix A using */
/* > the Aasen's algorithm. The panel consists of a set of NB rows of A */
/* > when UPLO is U, or a set of NB columns when UPLO is L. */
/* > */
/* > In order to factorize the panel, the Aasen's algorithm requires the */
/* > last row, or column, of the previous panel. The first row, or column, */
/* > of A is set to be the first row, or column, of an identity matrix, */
/* > which is used to factorize the first panel. */
/* > */
/* > The resulting J-th row of U, or J-th column of L, is stored in the */
/* > (J-1)-th row, or column, of A (without the unit diagonals), while */
/* > the diagonal and subdiagonal of A are overwritten by those of T. */
/* > */
/* > \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] J1 */
/* > \verbatim */
/* >          J1 is INTEGER */
/* >          The location of the first row, or column, of the panel */
/* >          within the submatrix of A, passed to this routine, e.g., */
/* >          when called by CHETRF_AA, for the first panel, J1 is 1, */
/* >          while for the remaining panels, J1 is 2. */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The dimension of the submatrix. M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NB */
/* > \verbatim */
/* >          NB is INTEGER */
/* >          The dimension of the panel to be facotorized. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is COMPLEX array, dimension (LDA,M) for */
/* >          the first panel, while dimension (LDA,M+1) for the */
/* >          remaining panels. */
/* > */
/* >          On entry, A contains the last row, or column, of */
/* >          the previous panel, and the trailing submatrix of A */
/* >          to be factorized, except for the first panel, only */
/* >          the panel is passed. */
/* > */
/* >          On exit, the leading panel is factorized. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] IPIV */
/* > \verbatim */
/* >          IPIV is INTEGER array, dimension (N) */
/* >          Details of the row and column interchanges, */
/* >          the row and column k were interchanged with the row and */
/* >          column IPIV(k). */
/* > \endverbatim */
/* > */
/* > \param[in,out] H */
/* > \verbatim */
/* >          H is COMPLEX workspace, dimension (LDH,NB). */
/* > */
/* > \endverbatim */
/* > */
/* > \param[in] LDH */
/* > \verbatim */
/* >          LDH is INTEGER */
/* >          The leading dimension of the workspace H. LDH >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is COMPLEX workspace, dimension (M). */
/* > \endverbatim */
/* > */

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

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

/* > \date November 2017 */

/* > \ingroup complexSYcomputational */

/*  ===================================================================== */
/* Subroutine */ void clahef_aa_(char *uplo, integer *j1, integer *m, integer 
	*nb, complex *a, integer *lda, integer *ipiv, complex *h__, integer *
	ldh, complex *work)
{
    /* System generated locals */
    integer a_dim1, a_offset, h_dim1, h_offset, i__1, i__2;
    real r__1;
    complex q__1, q__2;

    /* Local variables */
    integer j, k;
    complex alpha;
    extern /* Subroutine */ void cscal_(integer *, complex *, complex *, 
	    integer *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ void cgemv_(char *, integer *, integer *, complex *
	    , complex *, integer *, complex *, integer *, complex *, complex *
	    , integer *), ccopy_(integer *, complex *, integer *, 
	    complex *, integer *), cswap_(integer *, complex *, integer *, 
	    complex *, integer *), caxpy_(integer *, complex *, complex *, 
	    integer *, complex *, integer *);
    integer i1, k1, i2, mj;
    extern /* Subroutine */ void clacgv_(integer *, complex *, integer *);
    extern integer icamax_(integer *, complex *, integer *);
    extern /* Subroutine */ void claset_(char *, integer *, integer *, complex 
	    *, complex *, complex *, integer *);
    complex 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 */



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


    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --ipiv;
    h_dim1 = *ldh;
    h_offset = 1 + h_dim1 * 1;
    h__ -= h_offset;
    --work;

    /* Function Body */
    j = 1;

/*     K1 is the first column of the panel to be factorized */
/*     i.e.,  K1 is 2 for the first block column, and 1 for the rest of the blocks */

    k1 = 2 - *j1 + 1;

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

/*        ..................................................... */
/*        Factorize A as U**T*D*U using the upper triangle of A */
/*        ..................................................... */

L10:
	if (j > f2cmin(*m,*nb)) {
	    goto L20;
	}

/*        K is the column to be factorized */
/*         when being called from CHETRF_AA, */
/*         > for the first block column, J1 is 1, hence J1+J-1 is J, */
/*         > for the rest of the columns, J1 is 2, and J1+J-1 is J+1, */

	k = *j1 + j - 1;
	if (j == *m) {

/*            Only need to compute T(J, J) */

	    mj = 1;
	} else {
	    mj = *m - j + 1;
	}

/*        H(J:N, J) := A(J, J:N) - H(J:N, 1:(J-1)) * L(J1:(J-1), J), */
/*         where H(J:N, J) has been initialized to be A(J, J:N) */

	if (k > 2) {

/*        K is the column to be factorized */
/*         > for the first block column, K is J, skipping the first two */
/*           columns */
/*         > for the rest of the columns, K is J+1, skipping only the */
/*           first column */

	    i__1 = j - k1;
	    clacgv_(&i__1, &a[j * a_dim1 + 1], &c__1);
	    i__1 = j - k1;
	    q__1.r = -1.f, q__1.i = 0.f;
	    cgemv_("No transpose", &mj, &i__1, &q__1, &h__[j + k1 * h_dim1], 
		    ldh, &a[j * a_dim1 + 1], &c__1, &c_b2, &h__[j + j * 
		    h_dim1], &c__1);
	    i__1 = j - k1;
	    clacgv_(&i__1, &a[j * a_dim1 + 1], &c__1);
	}

/*        Copy H(i:n, i) into WORK */

	ccopy_(&mj, &h__[j + j * h_dim1], &c__1, &work[1], &c__1);

	if (j > k1) {

/*           Compute WORK := WORK - L(J-1, J:N) * T(J-1,J), */
/*            where A(J-1, J) stores T(J-1, J) and A(J-2, J:N) stores U(J-1, J:N) */

	    r_cnjg(&q__2, &a[k - 1 + j * a_dim1]);
	    q__1.r = -q__2.r, q__1.i = -q__2.i;
	    alpha.r = q__1.r, alpha.i = q__1.i;
	    caxpy_(&mj, &alpha, &a[k - 2 + j * a_dim1], lda, &work[1], &c__1);
	}

/*        Set A(J, J) = T(J, J) */

	i__1 = k + j * a_dim1;
	r__1 = work[1].r;
	a[i__1].r = r__1, a[i__1].i = 0.f;

	if (j < *m) {

/*           Compute WORK(2:N) = T(J, J) L(J, (J+1):N) */
/*            where A(J, J) stores T(J, J) and A(J-1, (J+1):N) stores U(J, (J+1):N) */

	    if (k > 1) {
		i__1 = k + j * a_dim1;
		q__1.r = -a[i__1].r, q__1.i = -a[i__1].i;
		alpha.r = q__1.r, alpha.i = q__1.i;
		i__1 = *m - j;
		caxpy_(&i__1, &alpha, &a[k - 1 + (j + 1) * a_dim1], lda, &
			work[2], &c__1);
	    }

/*           Find f2cmax(|WORK(2:n)|) */

	    i__1 = *m - j;
	    i2 = icamax_(&i__1, &work[2], &c__1) + 1;
	    i__1 = i2;
	    piv.r = work[i__1].r, piv.i = work[i__1].i;

/*           Apply hermitian pivot */

	    if (i2 != 2 && (piv.r != 0.f || piv.i != 0.)) {

/*              Swap WORK(I1) and WORK(I2) */

		i1 = 2;
		i__1 = i2;
		i__2 = i1;
		work[i__1].r = work[i__2].r, work[i__1].i = work[i__2].i;
		i__1 = i1;
		work[i__1].r = piv.r, work[i__1].i = piv.i;

/*              Swap A(I1, I1+1:N) with A(I1+1:N, I2) */

		i1 = i1 + j - 1;
		i2 = i2 + j - 1;
		i__1 = i2 - i1 - 1;
		cswap_(&i__1, &a[*j1 + i1 - 1 + (i1 + 1) * a_dim1], lda, &a[*
			j1 + i1 + i2 * a_dim1], &c__1);
		i__1 = i2 - i1;
		clacgv_(&i__1, &a[*j1 + i1 - 1 + (i1 + 1) * a_dim1], lda);
		i__1 = i2 - i1 - 1;
		clacgv_(&i__1, &a[*j1 + i1 + i2 * a_dim1], &c__1);

/*              Swap A(I1, I2+1:N) with A(I2, I2+1:N) */

		if (i2 < *m) {
		    i__1 = *m - i2;
		    cswap_(&i__1, &a[*j1 + i1 - 1 + (i2 + 1) * a_dim1], lda, &
			    a[*j1 + i2 - 1 + (i2 + 1) * a_dim1], lda);
		}

/*              Swap A(I1, I1) with A(I2,I2) */

		i__1 = i1 + *j1 - 1 + i1 * a_dim1;
		piv.r = a[i__1].r, piv.i = a[i__1].i;
		i__1 = *j1 + i1 - 1 + i1 * a_dim1;
		i__2 = *j1 + i2 - 1 + i2 * a_dim1;
		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
		i__1 = *j1 + i2 - 1 + i2 * a_dim1;
		a[i__1].r = piv.r, a[i__1].i = piv.i;

/*              Swap H(I1, 1:J1) with H(I2, 1:J1) */

		i__1 = i1 - 1;
		cswap_(&i__1, &h__[i1 + h_dim1], ldh, &h__[i2 + h_dim1], ldh);
		ipiv[i1] = i2;

		if (i1 > k1 - 1) {

/*                 Swap L(1:I1-1, I1) with L(1:I1-1, I2), */
/*                  skipping the first column */

		    i__1 = i1 - k1 + 1;
		    cswap_(&i__1, &a[i1 * a_dim1 + 1], &c__1, &a[i2 * a_dim1 
			    + 1], &c__1);
		}
	    } else {
		ipiv[j + 1] = j + 1;
	    }

/*           Set A(J, J+1) = T(J, J+1) */

	    i__1 = k + (j + 1) * a_dim1;
	    a[i__1].r = work[2].r, a[i__1].i = work[2].i;

	    if (j < *nb) {

/*              Copy A(J+1:N, J+1) into H(J:N, J), */

		i__1 = *m - j;
		ccopy_(&i__1, &a[k + 1 + (j + 1) * a_dim1], lda, &h__[j + 1 + 
			(j + 1) * h_dim1], &c__1);
	    }

/*           Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1), */
/*            where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1) */

	    if (j < *m - 1) {
		i__1 = k + (j + 1) * a_dim1;
		if (a[i__1].r != 0.f || a[i__1].i != 0.f) {
		    c_div(&q__1, &c_b2, &a[k + (j + 1) * a_dim1]);
		    alpha.r = q__1.r, alpha.i = q__1.i;
		    i__1 = *m - j - 1;
		    ccopy_(&i__1, &work[3], &c__1, &a[k + (j + 2) * a_dim1], 
			    lda);
		    i__1 = *m - j - 1;
		    cscal_(&i__1, &alpha, &a[k + (j + 2) * a_dim1], lda);
		} else {
		    i__1 = *m - j - 1;
		    claset_("Full", &c__1, &i__1, &c_b1, &c_b1, &a[k + (j + 2)
			     * a_dim1], lda);
		}
	    }
	}
	++j;
	goto L10;
L20:

	;
    } else {

/*        ..................................................... */
/*        Factorize A as L*D*L**T using the lower triangle of A */
/*        ..................................................... */

L30:
	if (j > f2cmin(*m,*nb)) {
	    goto L40;
	}

/*        K is the column to be factorized */
/*         when being called from CHETRF_AA, */
/*         > for the first block column, J1 is 1, hence J1+J-1 is J, */
/*         > for the rest of the columns, J1 is 2, and J1+J-1 is J+1, */

	k = *j1 + j - 1;
	if (j == *m) {

/*            Only need to compute T(J, J) */

	    mj = 1;
	} else {
	    mj = *m - j + 1;
	}

/*        H(J:N, J) := A(J:N, J) - H(J:N, 1:(J-1)) * L(J, J1:(J-1))^T, */
/*         where H(J:N, J) has been initialized to be A(J:N, J) */

	if (k > 2) {

/*        K is the column to be factorized */
/*         > for the first block column, K is J, skipping the first two */
/*           columns */
/*         > for the rest of the columns, K is J+1, skipping only the */
/*           first column */

	    i__1 = j - k1;
	    clacgv_(&i__1, &a[j + a_dim1], lda);
	    i__1 = j - k1;
	    q__1.r = -1.f, q__1.i = 0.f;
	    cgemv_("No transpose", &mj, &i__1, &q__1, &h__[j + k1 * h_dim1], 
		    ldh, &a[j + a_dim1], lda, &c_b2, &h__[j + j * h_dim1], &
		    c__1);
	    i__1 = j - k1;
	    clacgv_(&i__1, &a[j + a_dim1], lda);
	}

/*        Copy H(J:N, J) into WORK */

	ccopy_(&mj, &h__[j + j * h_dim1], &c__1, &work[1], &c__1);

	if (j > k1) {

/*           Compute WORK := WORK - L(J:N, J-1) * T(J-1,J), */
/*            where A(J-1, J) = T(J-1, J) and A(J, J-2) = L(J, J-1) */

	    r_cnjg(&q__2, &a[j + (k - 1) * a_dim1]);
	    q__1.r = -q__2.r, q__1.i = -q__2.i;
	    alpha.r = q__1.r, alpha.i = q__1.i;
	    caxpy_(&mj, &alpha, &a[j + (k - 2) * a_dim1], &c__1, &work[1], &
		    c__1);
	}

/*        Set A(J, J) = T(J, J) */

	i__1 = j + k * a_dim1;
	r__1 = work[1].r;
	a[i__1].r = r__1, a[i__1].i = 0.f;

	if (j < *m) {

/*           Compute WORK(2:N) = T(J, J) L((J+1):N, J) */
/*            where A(J, J) = T(J, J) and A((J+1):N, J-1) = L((J+1):N, J) */

	    if (k > 1) {
		i__1 = j + k * a_dim1;
		q__1.r = -a[i__1].r, q__1.i = -a[i__1].i;
		alpha.r = q__1.r, alpha.i = q__1.i;
		i__1 = *m - j;
		caxpy_(&i__1, &alpha, &a[j + 1 + (k - 1) * a_dim1], &c__1, &
			work[2], &c__1);
	    }

/*           Find f2cmax(|WORK(2:n)|) */

	    i__1 = *m - j;
	    i2 = icamax_(&i__1, &work[2], &c__1) + 1;
	    i__1 = i2;
	    piv.r = work[i__1].r, piv.i = work[i__1].i;

/*           Apply hermitian pivot */

	    if (i2 != 2 && (piv.r != 0.f || piv.i != 0.)) {

/*              Swap WORK(I1) and WORK(I2) */

		i1 = 2;
		i__1 = i2;
		i__2 = i1;
		work[i__1].r = work[i__2].r, work[i__1].i = work[i__2].i;
		i__1 = i1;
		work[i__1].r = piv.r, work[i__1].i = piv.i;

/*              Swap A(I1+1:N, I1) with A(I2, I1+1:N) */

		i1 = i1 + j - 1;
		i2 = i2 + j - 1;
		i__1 = i2 - i1 - 1;
		cswap_(&i__1, &a[i1 + 1 + (*j1 + i1 - 1) * a_dim1], &c__1, &a[
			i2 + (*j1 + i1) * a_dim1], lda);
		i__1 = i2 - i1;
		clacgv_(&i__1, &a[i1 + 1 + (*j1 + i1 - 1) * a_dim1], &c__1);
		i__1 = i2 - i1 - 1;
		clacgv_(&i__1, &a[i2 + (*j1 + i1) * a_dim1], lda);

/*              Swap A(I2+1:N, I1) with A(I2+1:N, I2) */

		if (i2 < *m) {
		    i__1 = *m - i2;
		    cswap_(&i__1, &a[i2 + 1 + (*j1 + i1 - 1) * a_dim1], &c__1,
			     &a[i2 + 1 + (*j1 + i2 - 1) * a_dim1], &c__1);
		}

/*              Swap A(I1, I1) with A(I2, I2) */

		i__1 = i1 + (*j1 + i1 - 1) * a_dim1;
		piv.r = a[i__1].r, piv.i = a[i__1].i;
		i__1 = i1 + (*j1 + i1 - 1) * a_dim1;
		i__2 = i2 + (*j1 + i2 - 1) * a_dim1;
		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
		i__1 = i2 + (*j1 + i2 - 1) * a_dim1;
		a[i__1].r = piv.r, a[i__1].i = piv.i;

/*              Swap H(I1, I1:J1) with H(I2, I2:J1) */

		i__1 = i1 - 1;
		cswap_(&i__1, &h__[i1 + h_dim1], ldh, &h__[i2 + h_dim1], ldh);
		ipiv[i1] = i2;

		if (i1 > k1 - 1) {

/*                 Swap L(1:I1-1, I1) with L(1:I1-1, I2), */
/*                  skipping the first column */

		    i__1 = i1 - k1 + 1;
		    cswap_(&i__1, &a[i1 + a_dim1], lda, &a[i2 + a_dim1], lda);
		}
	    } else {
		ipiv[j + 1] = j + 1;
	    }

/*           Set A(J+1, J) = T(J+1, J) */

	    i__1 = j + 1 + k * a_dim1;
	    a[i__1].r = work[2].r, a[i__1].i = work[2].i;

	    if (j < *nb) {

/*              Copy A(J+1:N, J+1) into H(J+1:N, J), */

		i__1 = *m - j;
		ccopy_(&i__1, &a[j + 1 + (k + 1) * a_dim1], &c__1, &h__[j + 1 
			+ (j + 1) * h_dim1], &c__1);
	    }

/*           Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1), */
/*            where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1) */

	    if (j < *m - 1) {
		i__1 = j + 1 + k * a_dim1;
		if (a[i__1].r != 0.f || a[i__1].i != 0.f) {
		    c_div(&q__1, &c_b2, &a[j + 1 + k * a_dim1]);
		    alpha.r = q__1.r, alpha.i = q__1.i;
		    i__1 = *m - j - 1;
		    ccopy_(&i__1, &work[3], &c__1, &a[j + 2 + k * a_dim1], &
			    c__1);
		    i__1 = *m - j - 1;
		    cscal_(&i__1, &alpha, &a[j + 2 + k * a_dim1], &c__1);
		} else {
		    i__1 = *m - j - 1;
		    claset_("Full", &i__1, &c__1, &c_b1, &c_b1, &a[j + 2 + k *
			     a_dim1], lda);
		}
	    }
	}
	++j;
	goto L30;
L40:
	;
    }
    return;

/*     End of CLAHEF_AA */

} /* clahef_aa__ */