OpenBLAS/lapack-netlib/SRC/zcposv.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 doublecomplex c_b1 = {-1.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;

/* > \brief <b> ZCPOSV computes the solution to system of linear equations A * X = B for PO matrices</b> */

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

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

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

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

/*       SUBROUTINE ZCPOSV( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, */
/*                          SWORK, RWORK, ITER, INFO ) */

/*       CHARACTER          UPLO */
/*       INTEGER            INFO, ITER, LDA, LDB, LDX, N, NRHS */
/*       DOUBLE PRECISION   RWORK( * ) */
/*       COMPLEX            SWORK( * ) */
/*       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( N, * ), */
/*      $                   X( LDX, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > ZCPOSV computes the solution to a complex system of linear equations */
/* >    A * X = B, */
/* > where A is an N-by-N Hermitian positive definite matrix and X and B */
/* > are N-by-NRHS matrices. */
/* > */
/* > ZCPOSV first attempts to factorize the matrix in COMPLEX and use this */
/* > factorization within an iterative refinement procedure to produce a */
/* > solution with COMPLEX*16 normwise backward error quality (see below). */
/* > If the approach fails the method switches to a COMPLEX*16 */
/* > factorization and solve. */
/* > */
/* > The iterative refinement is not going to be a winning strategy if */
/* > the ratio COMPLEX performance over COMPLEX*16 performance is too */
/* > small. A reasonable strategy should take the number of right-hand */
/* > sides and the size of the matrix into account. This might be done */
/* > with a call to ILAENV in the future. Up to now, we always try */
/* > iterative refinement. */
/* > */
/* > The iterative refinement process is stopped if */
/* >     ITER > ITERMAX */
/* > or for all the RHS we have: */
/* >     RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX */
/* > where */
/* >     o ITER is the number of the current iteration in the iterative */
/* >       refinement process */
/* >     o RNRM is the infinity-norm of the residual */
/* >     o XNRM is the infinity-norm of the solution */
/* >     o ANRM is the infinity-operator-norm of the matrix A */
/* >     o EPS is the machine epsilon returned by DLAMCH('Epsilon') */
/* > The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 */
/* > respectively. */
/* > \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 number of linear equations, i.e., the order of the */
/* >          matrix A.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NRHS */
/* > \verbatim */
/* >          NRHS is INTEGER */
/* >          The number of right hand sides, i.e., the number of columns */
/* >          of the matrix B.  NRHS >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is COMPLEX*16 array, */
/* >          dimension (LDA,N) */
/* >          On entry, the Hermitian 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. */
/* > */
/* >          Note that the imaginary parts of the diagonal */
/* >          elements need not be set and are assumed to be zero. */
/* > */
/* >          On exit, if iterative refinement has been successfully used */
/* >          (INFO = 0 and ITER >= 0, see description below), then A is */
/* >          unchanged, if double precision factorization has been used */
/* >          (INFO = 0 and ITER < 0, see description below), then the */
/* >          array A contains the factor U or L from the Cholesky */
/* >          factorization A = U**H*U or A = L*L**H. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] B */
/* > \verbatim */
/* >          B is COMPLEX*16 array, dimension (LDB,NRHS) */
/* >          The N-by-NRHS right hand side matrix B. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* >          LDB is INTEGER */
/* >          The leading dimension of the array B.  LDB >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] X */
/* > \verbatim */
/* >          X is COMPLEX*16 array, dimension (LDX,NRHS) */
/* >          If INFO = 0, the N-by-NRHS solution matrix X. */
/* > \endverbatim */
/* > */
/* > \param[in] LDX */
/* > \verbatim */
/* >          LDX is INTEGER */
/* >          The leading dimension of the array X.  LDX >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is COMPLEX*16 array, dimension (N,NRHS) */
/* >          This array is used to hold the residual vectors. */
/* > \endverbatim */
/* > */
/* > \param[out] SWORK */
/* > \verbatim */
/* >          SWORK is COMPLEX array, dimension (N*(N+NRHS)) */
/* >          This array is used to use the single precision matrix and the */
/* >          right-hand sides or solutions in single precision. */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* >          RWORK is DOUBLE PRECISION array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] ITER */
/* > \verbatim */
/* >          ITER is INTEGER */
/* >          < 0: iterative refinement has failed, COMPLEX*16 */
/* >               factorization has been performed */
/* >               -1 : the routine fell back to full precision for */
/* >                    implementation- or machine-specific reasons */
/* >               -2 : narrowing the precision induced an overflow, */
/* >                    the routine fell back to full precision */
/* >               -3 : failure of CPOTRF */
/* >               -31: stop the iterative refinement after the 30th */
/* >                    iterations */
/* >          > 0: iterative refinement has been successfully used. */
/* >               Returns the number of iterations */
/* > \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 of */
/* >                (COMPLEX*16) A is not positive definite, so the */
/* >                factorization could not be completed, and the solution */
/* >                has not been computed. */
/* > \endverbatim */

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

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

/* > \date June 2016 */

/* > \ingroup complex16POsolve */

/*  ===================================================================== */
/* Subroutine */ void zcposv_(char *uplo, integer *n, integer *nrhs, 
	doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
	doublecomplex *x, integer *ldx, doublecomplex *work, complex *swork, 
	doublereal *rwork, integer *iter, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, work_dim1, work_offset, 
	    x_dim1, x_offset, i__1, i__2;
    doublereal d__1, d__2;

    /* Local variables */
    doublereal anrm;
    integer ptsa;
    doublereal rnrm, xnrm;
    integer ptsx, i__;
    extern logical lsame_(char *, char *);
    integer iiter;
    extern /* Subroutine */ void zhemm_(char *, char *, integer *, integer *, 
	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
	    integer *, doublecomplex *, doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, doublecomplex *, 
	    integer *, doublecomplex *, integer *), zlag2c_(integer *, 
	    integer *, doublecomplex *, integer *, complex *, integer *, 
	    integer *), clag2z_(integer *, integer *, complex *, integer *, 
	    doublecomplex *, integer *, integer *), zlat2c_(char *, integer *,
	     doublecomplex *, integer *, complex *, integer *, integer *);
    extern doublereal dlamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, 
	    integer *, doublereal *);
    extern integer izamax_(integer *, doublecomplex *, integer *);
    extern /* Subroutine */ int cpotrf_(char *, integer *, complex *, integer 
	    *, integer *);
    extern void zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *), 
	    cpotrs_(char *, integer *, integer *, complex *, integer *, 
	    complex *, integer *, integer *);
    extern int zpotrf_(char *, integer 
	    *, doublecomplex *, integer *, integer *);
    extern void zpotrs_(char *,
	     integer *, integer *, doublecomplex *, integer *, doublecomplex *
	    , integer *, integer *);
    doublereal cte, eps;


/*  -- LAPACK driver 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..-- */
/*     June 2016 */


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







    /* Parameter adjustments */
    work_dim1 = *n;
    work_offset = 1 + work_dim1 * 1;
    work -= work_offset;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1 * 1;
    x -= x_offset;
    --swork;
    --rwork;

    /* Function Body */
    *info = 0;
    *iter = 0;

/*     Test the input parameters. */

    if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*nrhs < 0) {
	*info = -3;
    } else if (*lda < f2cmax(1,*n)) {
	*info = -5;
    } else if (*ldb < f2cmax(1,*n)) {
	*info = -7;
    } else if (*ldx < f2cmax(1,*n)) {
	*info = -9;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZCPOSV", &i__1, (ftnlen)6);
	return;
    }

/*     Quick return if (N.EQ.0). */

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

/*     Skip single precision iterative refinement if a priori slower */
/*     than double precision factorization. */

    if (FALSE_) {
	*iter = -1;
	goto L40;
    }

/*     Compute some constants. */

    anrm = zlanhe_("I", uplo, n, &a[a_offset], lda, &rwork[1]);
    eps = dlamch_("Epsilon");
    cte = anrm * eps * sqrt((doublereal) (*n)) * 1.;

/*     Set the indices PTSA, PTSX for referencing SA and SX in SWORK. */

    ptsa = 1;
    ptsx = ptsa + *n * *n;

/*     Convert B from double precision to single precision and store the */
/*     result in SX. */

    zlag2c_(n, nrhs, &b[b_offset], ldb, &swork[ptsx], n, info);

    if (*info != 0) {
	*iter = -2;
	goto L40;
    }

/*     Convert A from double precision to single precision and store the */
/*     result in SA. */

    zlat2c_(uplo, n, &a[a_offset], lda, &swork[ptsa], n, info);

    if (*info != 0) {
	*iter = -2;
	goto L40;
    }

/*     Compute the Cholesky factorization of SA. */

    cpotrf_(uplo, n, &swork[ptsa], n, info);

    if (*info != 0) {
	*iter = -3;
	goto L40;
    }

/*     Solve the system SA*SX = SB. */

    cpotrs_(uplo, n, nrhs, &swork[ptsa], n, &swork[ptsx], n, info);

/*     Convert SX back to COMPLEX*16 */

    clag2z_(n, nrhs, &swork[ptsx], n, &x[x_offset], ldx, info);

/*     Compute R = B - AX (R is WORK). */

    zlacpy_("All", n, nrhs, &b[b_offset], ldb, &work[work_offset], n);

    zhemm_("Left", uplo, n, nrhs, &c_b1, &a[a_offset], lda, &x[x_offset], ldx,
	     &c_b2, &work[work_offset], n);

/*     Check whether the NRHS normwise backward errors satisfy the */
/*     stopping criterion. If yes, set ITER=0 and return. */

    i__1 = *nrhs;
    for (i__ = 1; i__ <= i__1; ++i__) {
	i__2 = izamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ * x_dim1;
	xnrm = (d__1 = x[i__2].r, abs(d__1)) + (d__2 = d_imag(&x[izamax_(n, &
		x[i__ * x_dim1 + 1], &c__1) + i__ * x_dim1]), abs(d__2));
	i__2 = izamax_(n, &work[i__ * work_dim1 + 1], &c__1) + i__ * 
		work_dim1;
	rnrm = (d__1 = work[i__2].r, abs(d__1)) + (d__2 = d_imag(&work[
		izamax_(n, &work[i__ * work_dim1 + 1], &c__1) + i__ * 
		work_dim1]), abs(d__2));
	if (rnrm > xnrm * cte) {
	    goto L10;
	}
    }

/*     If we are here, the NRHS normwise backward errors satisfy the */
/*     stopping criterion. We are good to exit. */

    *iter = 0;
    return;

L10:

    for (iiter = 1; iiter <= 30; ++iiter) {

/*        Convert R (in WORK) from double precision to single precision */
/*        and store the result in SX. */

	zlag2c_(n, nrhs, &work[work_offset], n, &swork[ptsx], n, info);

	if (*info != 0) {
	    *iter = -2;
	    goto L40;
	}

/*        Solve the system SA*SX = SR. */

	cpotrs_(uplo, n, nrhs, &swork[ptsa], n, &swork[ptsx], n, info);

/*        Convert SX back to double precision and update the current */
/*        iterate. */

	clag2z_(n, nrhs, &swork[ptsx], n, &work[work_offset], n, info);

	i__1 = *nrhs;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    zaxpy_(n, &c_b2, &work[i__ * work_dim1 + 1], &c__1, &x[i__ * 
		    x_dim1 + 1], &c__1);
	}

/*        Compute R = B - AX (R is WORK). */

	zlacpy_("All", n, nrhs, &b[b_offset], ldb, &work[work_offset], n);

	zhemm_("L", uplo, n, nrhs, &c_b1, &a[a_offset], lda, &x[x_offset], 
		ldx, &c_b2, &work[work_offset], n);

/*        Check whether the NRHS normwise backward errors satisfy the */
/*        stopping criterion. If yes, set ITER=IITER>0 and return. */

	i__1 = *nrhs;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    i__2 = izamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ * x_dim1;
	    xnrm = (d__1 = x[i__2].r, abs(d__1)) + (d__2 = d_imag(&x[izamax_(
		    n, &x[i__ * x_dim1 + 1], &c__1) + i__ * x_dim1]), abs(
		    d__2));
	    i__2 = izamax_(n, &work[i__ * work_dim1 + 1], &c__1) + i__ * 
		    work_dim1;
	    rnrm = (d__1 = work[i__2].r, abs(d__1)) + (d__2 = d_imag(&work[
		    izamax_(n, &work[i__ * work_dim1 + 1], &c__1) + i__ * 
		    work_dim1]), abs(d__2));
	    if (rnrm > xnrm * cte) {
		goto L20;
	    }
	}

/*        If we are here, the NRHS normwise backward errors satisfy the */
/*        stopping criterion, we are good to exit. */

	*iter = iiter;

	return;

L20:

/* L30: */
	;
    }

/*     If we are at this place of the code, this is because we have */
/*     performed ITER=ITERMAX iterations and never satisfied the */
/*     stopping criterion, set up the ITER flag accordingly and follow */
/*     up on double precision routine. */

    *iter = -31;

L40:

/*     Single-precision iterative refinement failed to converge to a */
/*     satisfactory solution, so we resort to double precision. */

    zpotrf_(uplo, n, &a[a_offset], lda, info);

    if (*info != 0) {
	return;
    }

    zlacpy_("All", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    zpotrs_(uplo, n, nrhs, &a[a_offset], lda, &x[x_offset], ldx, info);

    return;

/*     End of ZCPOSV. */

} /* zcposv_ */