OpenBLAS/lapack-netlib/SRC/dlatdf.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 integer c__1 = 1;
static integer c_n1 = -1;
static doublereal c_b23 = 1.;
static doublereal c_b37 = -1.;

/* > \brief \b DLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contrib
ution to the reciprocal Dif-estimate. */

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

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

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

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

/*       SUBROUTINE DLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, */
/*                          JPIV ) */

/*       INTEGER            IJOB, LDZ, N */
/*       DOUBLE PRECISION   RDSCAL, RDSUM */
/*       INTEGER            IPIV( * ), JPIV( * ) */
/*       DOUBLE PRECISION   RHS( * ), Z( LDZ, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLATDF uses the LU factorization of the n-by-n matrix Z computed by */
/* > DGETC2 and computes a contribution to the reciprocal Dif-estimate */
/* > by solving Z * x = b for x, and choosing the r.h.s. b such that */
/* > the norm of x is as large as possible. On entry RHS = b holds the */
/* > contribution from earlier solved sub-systems, and on return RHS = x. */
/* > */
/* > The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q, */
/* > where P and Q are permutation matrices. L is lower triangular with */
/* > unit diagonal elements and U is upper triangular. */
/* > \endverbatim */

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

/* > \param[in] IJOB */
/* > \verbatim */
/* >          IJOB is INTEGER */
/* >          IJOB = 2: First compute an approximative null-vector e */
/* >              of Z using DGECON, e is normalized and solve for */
/* >              Zx = +-e - f with the sign giving the greater value */
/* >              of 2-norm(x). About 5 times as expensive as Default. */
/* >          IJOB .ne. 2: Local look ahead strategy where all entries of */
/* >              the r.h.s. b is chosen as either +1 or -1 (Default). */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The number of columns of the matrix Z. */
/* > \endverbatim */
/* > */
/* > \param[in] Z */
/* > \verbatim */
/* >          Z is DOUBLE PRECISION array, dimension (LDZ, N) */
/* >          On entry, the LU part of the factorization of the n-by-n */
/* >          matrix Z computed by DGETC2:  Z = P * L * U * Q */
/* > \endverbatim */
/* > */
/* > \param[in] LDZ */
/* > \verbatim */
/* >          LDZ is INTEGER */
/* >          The leading dimension of the array Z.  LDA >= f2cmax(1, N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] RHS */
/* > \verbatim */
/* >          RHS is DOUBLE PRECISION array, dimension (N) */
/* >          On entry, RHS contains contributions from other subsystems. */
/* >          On exit, RHS contains the solution of the subsystem with */
/* >          entries according to the value of IJOB (see above). */
/* > \endverbatim */
/* > */
/* > \param[in,out] RDSUM */
/* > \verbatim */
/* >          RDSUM is DOUBLE PRECISION */
/* >          On entry, the sum of squares of computed contributions to */
/* >          the Dif-estimate under computation by DTGSYL, where the */
/* >          scaling factor RDSCAL (see below) has been factored out. */
/* >          On exit, the corresponding sum of squares updated with the */
/* >          contributions from the current sub-system. */
/* >          If TRANS = 'T' RDSUM is not touched. */
/* >          NOTE: RDSUM only makes sense when DTGSY2 is called by STGSYL. */
/* > \endverbatim */
/* > */
/* > \param[in,out] RDSCAL */
/* > \verbatim */
/* >          RDSCAL is DOUBLE PRECISION */
/* >          On entry, scaling factor used to prevent overflow in RDSUM. */
/* >          On exit, RDSCAL is updated w.r.t. the current contributions */
/* >          in RDSUM. */
/* >          If TRANS = 'T', RDSCAL is not touched. */
/* >          NOTE: RDSCAL only makes sense when DTGSY2 is called by */
/* >                DTGSYL. */
/* > \endverbatim */
/* > */
/* > \param[in] IPIV */
/* > \verbatim */
/* >          IPIV is INTEGER array, dimension (N). */
/* >          The pivot indices; for 1 <= i <= N, row i of the */
/* >          matrix has been interchanged with row IPIV(i). */
/* > \endverbatim */
/* > */
/* > \param[in] JPIV */
/* > \verbatim */
/* >          JPIV is INTEGER array, dimension (N). */
/* >          The pivot indices; for 1 <= j <= N, column j of the */
/* >          matrix has been interchanged with column JPIV(j). */
/* > \endverbatim */

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

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

/* > \date June 2016 */

/* > \ingroup doubleOTHERauxiliary */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* >  This routine is a further developed implementation of algorithm */
/* >  BSOLVE in [1] using complete pivoting in the LU factorization. */

/* > \par Contributors: */
/*  ================== */
/* > */
/* >     Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* >     Umea University, S-901 87 Umea, Sweden. */

/* > \par References: */
/*  ================ */
/* > */
/* > \verbatim */
/* > */
/* > */
/* >  [1] Bo Kagstrom and Lars Westin, */
/* >      Generalized Schur Methods with Condition Estimators for */
/* >      Solving the Generalized Sylvester Equation, IEEE Transactions */
/* >      on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751. */
/* > */
/* >  [2] Peter Poromaa, */
/* >      On Efficient and Robust Estimators for the Separation */
/* >      between two Regular Matrix Pairs with Applications in */
/* >      Condition Estimation. Report IMINF-95.05, Departement of */
/* >      Computing Science, Umea University, S-901 87 Umea, Sweden, 1995. */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ void dlatdf_(integer *ijob, integer *n, doublereal *z__, 
	integer *ldz, doublereal *rhs, doublereal *rdsum, doublereal *rdscal, 
	integer *ipiv, integer *jpiv)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1, i__2;
    doublereal d__1;

    /* Local variables */
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    integer info;
    doublereal temp, work[32];
    integer i__, j, k;
    extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    extern doublereal dasum_(integer *, doublereal *, integer *);
    doublereal pmone;
    extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *), daxpy_(integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *);
    doublereal sminu;
    integer iwork[8];
    doublereal splus;
    extern /* Subroutine */ void dgesc2_(integer *, doublereal *, integer *, 
	    doublereal *, integer *, integer *, doublereal *);
    doublereal bm, bp;
    extern /* Subroutine */ void dgecon_(char *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, doublereal *, integer *, 
	    integer *);
    doublereal xm[8], xp[8];
    extern /* Subroutine */ void dlassq_(integer *, doublereal *, integer *, 
	    doublereal *, doublereal *);
    extern int dlaswp_(integer *, doublereal *, 
	    integer *, integer *, integer *, integer *, integer *);


/*  -- LAPACK auxiliary routine (version 3.7.0) -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/*     June 2016 */


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


    /* Parameter adjustments */
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --rhs;
    --ipiv;
    --jpiv;

    /* Function Body */
    if (*ijob != 2) {

/*        Apply permutations IPIV to RHS */

	i__1 = *n - 1;
	dlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &ipiv[1], &c__1);

/*        Solve for L-part choosing RHS either to +1 or -1. */

	pmone = -1.;

	i__1 = *n - 1;
	for (j = 1; j <= i__1; ++j) {
	    bp = rhs[j] + 1.;
	    bm = rhs[j] - 1.;
	    splus = 1.;

/*           Look-ahead for L-part RHS(1:N-1) = + or -1, SPLUS and */
/*           SMIN computed more efficiently than in BSOLVE [1]. */

	    i__2 = *n - j;
	    splus += ddot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &z__[j + 1 
		    + j * z_dim1], &c__1);
	    i__2 = *n - j;
	    sminu = ddot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
		     &c__1);
	    splus *= rhs[j];
	    if (splus > sminu) {
		rhs[j] = bp;
	    } else if (sminu > splus) {
		rhs[j] = bm;
	    } else {

/*              In this case the updating sums are equal and we can */
/*              choose RHS(J) +1 or -1. The first time this happens */
/*              we choose -1, thereafter +1. This is a simple way to */
/*              get good estimates of matrices like Byers well-known */
/*              example (see [1]). (Not done in BSOLVE.) */

		rhs[j] += pmone;
		pmone = 1.;
	    }

/*           Compute the remaining r.h.s. */

	    temp = -rhs[j];
	    i__2 = *n - j;
	    daxpy_(&i__2, &temp, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
		     &c__1);

/* L10: */
	}

/*        Solve for U-part, look-ahead for RHS(N) = +-1. This is not done */
/*        in BSOLVE and will hopefully give us a better estimate because */
/*        any ill-conditioning of the original matrix is transferred to U */
/*        and not to L. U(N, N) is an approximation to sigma_min(LU). */

	i__1 = *n - 1;
	dcopy_(&i__1, &rhs[1], &c__1, xp, &c__1);
	xp[*n - 1] = rhs[*n] + 1.;
	rhs[*n] += -1.;
	splus = 0.;
	sminu = 0.;
	for (i__ = *n; i__ >= 1; --i__) {
	    temp = 1. / z__[i__ + i__ * z_dim1];
	    xp[i__ - 1] *= temp;
	    rhs[i__] *= temp;
	    i__1 = *n;
	    for (k = i__ + 1; k <= i__1; ++k) {
		xp[i__ - 1] -= xp[k - 1] * (z__[i__ + k * z_dim1] * temp);
		rhs[i__] -= rhs[k] * (z__[i__ + k * z_dim1] * temp);
/* L20: */
	    }
	    splus += (d__1 = xp[i__ - 1], abs(d__1));
	    sminu += (d__1 = rhs[i__], abs(d__1));
/* L30: */
	}
	if (splus > sminu) {
	    dcopy_(n, xp, &c__1, &rhs[1], &c__1);
	}

/*        Apply the permutations JPIV to the computed solution (RHS) */

	i__1 = *n - 1;
	dlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);

/*        Compute the sum of squares */

	dlassq_(n, &rhs[1], &c__1, rdscal, rdsum);

    } else {

/*        IJOB = 2, Compute approximate nullvector XM of Z */

	dgecon_("I", n, &z__[z_offset], ldz, &c_b23, &temp, work, iwork, &
		info);
	dcopy_(n, &work[*n], &c__1, xm, &c__1);

/*        Compute RHS */

	i__1 = *n - 1;
	dlaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
	temp = 1. / sqrt(ddot_(n, xm, &c__1, xm, &c__1));
	dscal_(n, &temp, xm, &c__1);
	dcopy_(n, xm, &c__1, xp, &c__1);
	daxpy_(n, &c_b23, &rhs[1], &c__1, xp, &c__1);
	daxpy_(n, &c_b37, xm, &c__1, &rhs[1], &c__1);
	dgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &temp);
	dgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &temp);
	if (dasum_(n, xp, &c__1) > dasum_(n, &rhs[1], &c__1)) {
	    dcopy_(n, xp, &c__1, &rhs[1], &c__1);
	}

/*        Compute the sum of squares */

	dlassq_(n, &rhs[1], &c__1, rdscal, rdsum);

    }

    return;

/*     End of DLATDF */

} /* dlatdf_ */