OpenBLAS/lapack-netlib/SRC/dggsvd3.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 int logical;
typedef short int shortlogical;
typedef char logical1;
typedef char integer1;

#define TRUE_ (1)
#define FALSE_ (0)

/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif

/* I/O stuff */

typedef int flag;
typedef int ftnlen;
typedef int ftnint;

/*external read, write*/
typedef struct
{	flag cierr;
	ftnint ciunit;
	flag ciend;
	char *cifmt;
	ftnint cirec;
} cilist;

/*internal read, write*/
typedef struct
{	flag icierr;
	char *iciunit;
	flag iciend;
	char *icifmt;
	ftnint icirlen;
	ftnint icirnum;
} icilist;

/*open*/
typedef struct
{	flag oerr;
	ftnint ounit;
	char *ofnm;
	ftnlen ofnmlen;
	char *osta;
	char *oacc;
	char *ofm;
	ftnint orl;
	char *oblnk;
} olist;

/*close*/
typedef struct
{	flag cerr;
	ftnint cunit;
	char *csta;
} cllist;

/*rewind, backspace, endfile*/
typedef struct
{	flag aerr;
	ftnint aunit;
} alist;

/* inquire */
typedef struct
{	flag inerr;
	ftnint inunit;
	char *infile;
	ftnlen infilen;
	ftnint	*inex;	/*parameters in standard's order*/
	ftnint	*inopen;
	ftnint	*innum;
	ftnint	*innamed;
	char	*inname;
	ftnlen	innamlen;
	char	*inacc;
	ftnlen	inacclen;
	char	*inseq;
	ftnlen	inseqlen;
	char 	*indir;
	ftnlen	indirlen;
	char	*infmt;
	ftnlen	infmtlen;
	char	*inform;
	ftnint	informlen;
	char	*inunf;
	ftnlen	inunflen;
	ftnint	*inrecl;
	ftnint	*innrec;
	char	*inblank;
	ftnlen	inblanklen;
} inlist;

#define VOID void

union Multitype {	/* for multiple entry points */
	integer1 g;
	shortint h;
	integer i;
	/* longint j; */
	real r;
	doublereal d;
	complex c;
	doublecomplex z;
	};

typedef union Multitype Multitype;

struct Vardesc {	/* for Namelist */
	char *name;
	char *addr;
	ftnlen *dims;
	int  type;
	};
typedef struct Vardesc Vardesc;

struct Namelist {
	char *name;
	Vardesc **vars;
	int nvars;
	};
typedef struct Namelist Namelist;

#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b)	((a) >> (b) & 1)
#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))

#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#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++ */

#define F2C_proc_par_types 1
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif

static float spow_ui(float x, integer n) {
	float pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
static double dpow_ui(double x, integer n) {
	double pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
#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_n1 = -1;
static integer c__1 = 1;

/* > \brief <b> DGGSVD3 computes the singular value decomposition (SVD) for OTHER matrices</b> */

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

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

/* > \htmlonly */
/* > Download DGGSVD3 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dggsvd3
.f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dggsvd3
.f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggsvd3
.f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

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

/*       SUBROUTINE DGGSVD3( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B, */
/*                           LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK, */
/*                           LWORK, IWORK, INFO ) */

/*       CHARACTER          JOBQ, JOBU, JOBV */
/*       INTEGER            INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P, LWORK */
/*       INTEGER            IWORK( * ) */
/*       DOUBLE PRECISION   A( LDA, * ), ALPHA( * ), B( LDB, * ), */
/*      $                   BETA( * ), Q( LDQ, * ), U( LDU, * ), */
/*      $                   V( LDV, * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DGGSVD3 computes the generalized singular value decomposition (GSVD) */
/* > of an M-by-N real matrix A and P-by-N real matrix B: */
/* > */
/* >       U**T*A*Q = D1*( 0 R ),    V**T*B*Q = D2*( 0 R ) */
/* > */
/* > where U, V and Q are orthogonal matrices. */
/* > Let K+L = the effective numerical rank of the matrix (A**T,B**T)**T, */
/* > then R is a K+L-by-K+L nonsingular upper triangular matrix, D1 and */
/* > D2 are M-by-(K+L) and P-by-(K+L) "diagonal" matrices and of the */
/* > following structures, respectively: */
/* > */
/* > If M-K-L >= 0, */
/* > */
/* >                     K  L */
/* >        D1 =     K ( I  0 ) */
/* >                 L ( 0  C ) */
/* >             M-K-L ( 0  0 ) */
/* > */
/* >                   K  L */
/* >        D2 =   L ( 0  S ) */
/* >             P-L ( 0  0 ) */
/* > */
/* >                 N-K-L  K    L */
/* >   ( 0 R ) = K (  0   R11  R12 ) */
/* >             L (  0    0   R22 ) */
/* > */
/* > where */
/* > */
/* >   C = diag( ALPHA(K+1), ... , ALPHA(K+L) ), */
/* >   S = diag( BETA(K+1),  ... , BETA(K+L) ), */
/* >   C**2 + S**2 = I. */
/* > */
/* >   R is stored in A(1:K+L,N-K-L+1:N) on exit. */
/* > */
/* > If M-K-L < 0, */
/* > */
/* >                   K M-K K+L-M */
/* >        D1 =   K ( I  0    0   ) */
/* >             M-K ( 0  C    0   ) */
/* > */
/* >                     K M-K K+L-M */
/* >        D2 =   M-K ( 0  S    0  ) */
/* >             K+L-M ( 0  0    I  ) */
/* >               P-L ( 0  0    0  ) */
/* > */
/* >                    N-K-L  K   M-K  K+L-M */
/* >   ( 0 R ) =     K ( 0    R11  R12  R13  ) */
/* >               M-K ( 0     0   R22  R23  ) */
/* >             K+L-M ( 0     0    0   R33  ) */
/* > */
/* > where */
/* > */
/* >   C = diag( ALPHA(K+1), ... , ALPHA(M) ), */
/* >   S = diag( BETA(K+1),  ... , BETA(M) ), */
/* >   C**2 + S**2 = I. */
/* > */
/* >   (R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N), and R33 is stored */
/* >   ( 0  R22 R23 ) */
/* >   in B(M-K+1:L,N+M-K-L+1:N) on exit. */
/* > */
/* > The routine computes C, S, R, and optionally the orthogonal */
/* > transformation matrices U, V and Q. */
/* > */
/* > In particular, if B is an N-by-N nonsingular matrix, then the GSVD of */
/* > A and B implicitly gives the SVD of A*inv(B): */
/* >                      A*inv(B) = U*(D1*inv(D2))*V**T. */
/* > If ( A**T,B**T)**T  has orthonormal columns, then the GSVD of A and B is */
/* > also equal to the CS decomposition of A and B. Furthermore, the GSVD */
/* > can be used to derive the solution of the eigenvalue problem: */
/* >                      A**T*A x = lambda* B**T*B x. */
/* > In some literature, the GSVD of A and B is presented in the form */
/* >                  U**T*A*X = ( 0 D1 ),   V**T*B*X = ( 0 D2 ) */
/* > where U and V are orthogonal and X is nonsingular, D1 and D2 are */
/* > ``diagonal''.  The former GSVD form can be converted to the latter */
/* > form by taking the nonsingular matrix X as */
/* > */
/* >                      X = Q*( I   0    ) */
/* >                            ( 0 inv(R) ). */
/* > \endverbatim */

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

/* > \param[in] JOBU */
/* > \verbatim */
/* >          JOBU is CHARACTER*1 */
/* >          = 'U':  Orthogonal matrix U is computed; */
/* >          = 'N':  U is not computed. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBV */
/* > \verbatim */
/* >          JOBV is CHARACTER*1 */
/* >          = 'V':  Orthogonal matrix V is computed; */
/* >          = 'N':  V is not computed. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBQ */
/* > \verbatim */
/* >          JOBQ is CHARACTER*1 */
/* >          = 'Q':  Orthogonal matrix Q is computed; */
/* >          = 'N':  Q is not computed. */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The number of rows of the matrix A.  M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The number of columns of the matrices A and B.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] P */
/* > \verbatim */
/* >          P is INTEGER */
/* >          The number of rows of the matrix B.  P >= 0. */
/* > \endverbatim */
/* > */
/* > \param[out] K */
/* > \verbatim */
/* >          K is INTEGER */
/* > \endverbatim */
/* > */
/* > \param[out] L */
/* > \verbatim */
/* >          L is INTEGER */
/* > */
/* >          On exit, K and L specify the dimension of the subblocks */
/* >          described in Purpose. */
/* >          K + L = effective numerical rank of (A**T,B**T)**T. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is DOUBLE PRECISION array, dimension (LDA,N) */
/* >          On entry, the M-by-N matrix A. */
/* >          On exit, A contains the triangular matrix R, or part of R. */
/* >          See Purpose for details. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A. LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* >          B is DOUBLE PRECISION array, dimension (LDB,N) */
/* >          On entry, the P-by-N matrix B. */
/* >          On exit, B contains the triangular matrix R if M-K-L < 0. */
/* >          See Purpose for details. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* >          LDB is INTEGER */
/* >          The leading dimension of the array B. LDB >= f2cmax(1,P). */
/* > \endverbatim */
/* > */
/* > \param[out] ALPHA */
/* > \verbatim */
/* >          ALPHA is DOUBLE PRECISION array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] BETA */
/* > \verbatim */
/* >          BETA is DOUBLE PRECISION array, dimension (N) */
/* > */
/* >          On exit, ALPHA and BETA contain the generalized singular */
/* >          value pairs of A and B; */
/* >            ALPHA(1:K) = 1, */
/* >            BETA(1:K)  = 0, */
/* >          and if M-K-L >= 0, */
/* >            ALPHA(K+1:K+L) = C, */
/* >            BETA(K+1:K+L)  = S, */
/* >          or if M-K-L < 0, */
/* >            ALPHA(K+1:M)=C, ALPHA(M+1:K+L)=0 */
/* >            BETA(K+1:M) =S, BETA(M+1:K+L) =1 */
/* >          and */
/* >            ALPHA(K+L+1:N) = 0 */
/* >            BETA(K+L+1:N)  = 0 */
/* > \endverbatim */
/* > */
/* > \param[out] U */
/* > \verbatim */
/* >          U is DOUBLE PRECISION array, dimension (LDU,M) */
/* >          If JOBU = 'U', U contains the M-by-M orthogonal matrix U. */
/* >          If JOBU = 'N', U is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* >          LDU is INTEGER */
/* >          The leading dimension of the array U. LDU >= f2cmax(1,M) if */
/* >          JOBU = 'U'; LDU >= 1 otherwise. */
/* > \endverbatim */
/* > */
/* > \param[out] V */
/* > \verbatim */
/* >          V is DOUBLE PRECISION array, dimension (LDV,P) */
/* >          If JOBV = 'V', V contains the P-by-P orthogonal matrix V. */
/* >          If JOBV = 'N', V is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDV */
/* > \verbatim */
/* >          LDV is INTEGER */
/* >          The leading dimension of the array V. LDV >= f2cmax(1,P) if */
/* >          JOBV = 'V'; LDV >= 1 otherwise. */
/* > \endverbatim */
/* > */
/* > \param[out] Q */
/* > \verbatim */
/* >          Q is DOUBLE PRECISION array, dimension (LDQ,N) */
/* >          If JOBQ = 'Q', Q contains the N-by-N orthogonal matrix Q. */
/* >          If JOBQ = 'N', Q is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDQ */
/* > \verbatim */
/* >          LDQ is INTEGER */
/* >          The leading dimension of the array Q. LDQ >= f2cmax(1,N) if */
/* >          JOBQ = 'Q'; LDQ >= 1 otherwise. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* >          LWORK is INTEGER */
/* >          The dimension of the array WORK. */
/* > */
/* >          If LWORK = -1, then a workspace query is assumed; the routine */
/* >          only calculates the optimal size of the WORK array, returns */
/* >          this value as the first entry of the WORK array, and no error */
/* >          message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (N) */
/* >          On exit, IWORK stores the sorting information. More */
/* >          precisely, the following loop will sort ALPHA */
/* >             for I = K+1, f2cmin(M,K+L) */
/* >                 swap ALPHA(I) and ALPHA(IWORK(I)) */
/* >             endfor */
/* >          such that ALPHA(1) >= ALPHA(2) >= ... >= ALPHA(N). */
/* > \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 = 1, the Jacobi-type procedure failed to */
/* >                converge.  For further details, see subroutine DTGSJA. */
/* > \endverbatim */

/* > \par Internal Parameters: */
/*  ========================= */
/* > */
/* > \verbatim */
/* >  TOLA    DOUBLE PRECISION */
/* >  TOLB    DOUBLE PRECISION */
/* >          TOLA and TOLB are the thresholds to determine the effective */
/* >          rank of (A**T,B**T)**T. Generally, they are set to */
/* >                   TOLA = MAX(M,N)*norm(A)*MACHEPS, */
/* >                   TOLB = MAX(P,N)*norm(B)*MACHEPS. */
/* >          The size of TOLA and TOLB may affect the size of backward */
/* >          errors of the decomposition. */
/* > \endverbatim */

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

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

/* > \date August 2015 */

/* > \ingroup doubleGEsing */

/* > \par Contributors: */
/*  ================== */
/* > */
/* >     Ming Gu and Huan Ren, Computer Science Division, University of */
/* >     California at Berkeley, USA */
/* > */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* >  DGGSVD3 replaces the deprecated subroutine DGGSVD. */
/* > */
/*  ===================================================================== */
/* Subroutine */ void dggsvd3_(char *jobu, char *jobv, char *jobq, integer *m, 
	integer *n, integer *p, integer *k, integer *l, doublereal *a, 
	integer *lda, doublereal *b, integer *ldb, doublereal *alpha, 
	doublereal *beta, doublereal *u, integer *ldu, doublereal *v, integer 
	*ldv, doublereal *q, integer *ldq, doublereal *work, integer *lwork, 
	integer *iwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1, 
	    u_offset, v_dim1, v_offset, i__1, i__2;

    /* Local variables */
    integer ibnd;
    doublereal tola;
    integer isub;
    doublereal tolb, unfl, temp, smax;
    integer ncallmycycle, i__, j;
    extern logical lsame_(char *, char *);
    doublereal anorm, bnorm;
    extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    logical wantq, wantu, wantv;
    extern doublereal dlamch_(char *), dlange_(char *, integer *, 
	    integer *, doublereal *, integer *, doublereal *);
    extern /* Subroutine */ void dtgsja_(char *, char *, char *, integer *, 
	    integer *, integer *, integer *, integer *, doublereal *, integer 
	    *, doublereal *, integer *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, integer *, doublereal *,
	     integer *, doublereal *, integer *, doublereal *, integer *, 
	    integer *);
    extern int xerbla_(char *, integer *, ftnlen);
    integer lwkopt;
    logical lquery;
    extern /* Subroutine */ void dggsvp3_(char *, char *, char *, integer *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
	    integer *, integer *, doublereal *, doublereal *, integer *, 
	    integer *);
    doublereal ulp;


/*  -- LAPACK driver 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..-- */
/*     August 2015 */


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


/*     Decode and test the input parameters */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --alpha;
    --beta;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1 * 1;
    u -= u_offset;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1 * 1;
    v -= v_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    --work;
    --iwork;

    /* Function Body */
    wantu = lsame_(jobu, "U");
    wantv = lsame_(jobv, "V");
    wantq = lsame_(jobq, "Q");
    lquery = *lwork == -1;
    lwkopt = 1;

/*     Test the input arguments */

    *info = 0;
    if (! (wantu || lsame_(jobu, "N"))) {
	*info = -1;
    } else if (! (wantv || lsame_(jobv, "N"))) {
	*info = -2;
    } else if (! (wantq || lsame_(jobq, "N"))) {
	*info = -3;
    } else if (*m < 0) {
	*info = -4;
    } else if (*n < 0) {
	*info = -5;
    } else if (*p < 0) {
	*info = -6;
    } else if (*lda < f2cmax(1,*m)) {
	*info = -10;
    } else if (*ldb < f2cmax(1,*p)) {
	*info = -12;
    } else if (*ldu < 1 || wantu && *ldu < *m) {
	*info = -16;
    } else if (*ldv < 1 || wantv && *ldv < *p) {
	*info = -18;
    } else if (*ldq < 1 || wantq && *ldq < *n) {
	*info = -20;
    } else if (*lwork < 1 && ! lquery) {
	*info = -24;
    }

/*     Compute workspace */

    if (*info == 0) {
	dggsvp3_(jobu, jobv, jobq, m, p, n, &a[a_offset], lda, &b[b_offset], 
		ldb, &tola, &tolb, k, l, &u[u_offset], ldu, &v[v_offset], ldv,
		 &q[q_offset], ldq, &iwork[1], &work[1], &work[1], &c_n1, 
		info);
	lwkopt = *n + (integer) work[1];
/* Computing MAX */
	i__1 = *n << 1;
	lwkopt = f2cmax(i__1,lwkopt);
	lwkopt = f2cmax(1,lwkopt);
	work[1] = (doublereal) lwkopt;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DGGSVD3", &i__1, (ftnlen)7);
	return;
    }
    if (lquery) {
	return;
    }

/*     Compute the Frobenius norm of matrices A and B */

    anorm = dlange_("1", m, n, &a[a_offset], lda, &work[1]);
    bnorm = dlange_("1", p, n, &b[b_offset], ldb, &work[1]);

/*     Get machine precision and set up threshold for determining */
/*     the effective numerical rank of the matrices A and B. */

    ulp = dlamch_("Precision");
    unfl = dlamch_("Safe Minimum");
    tola = f2cmax(*m,*n) * f2cmax(anorm,unfl) * ulp;
    tolb = f2cmax(*p,*n) * f2cmax(bnorm,unfl) * ulp;

/*     Preprocessing */

    i__1 = *lwork - *n;
    dggsvp3_(jobu, jobv, jobq, m, p, n, &a[a_offset], lda, &b[b_offset], ldb, 
	    &tola, &tolb, k, l, &u[u_offset], ldu, &v[v_offset], ldv, &q[
	    q_offset], ldq, &iwork[1], &work[1], &work[*n + 1], &i__1, info);

/*     Compute the GSVD of two upper "triangular" matrices */

    dtgsja_(jobu, jobv, jobq, m, p, n, k, l, &a[a_offset], lda, &b[b_offset], 
	    ldb, &tola, &tolb, &alpha[1], &beta[1], &u[u_offset], ldu, &v[
	    v_offset], ldv, &q[q_offset], ldq, &work[1], &ncallmycycle, info);

/*     Sort the singular values and store the pivot indices in IWORK */
/*     Copy ALPHA to WORK, then sort ALPHA in WORK */

    dcopy_(n, &alpha[1], &c__1, &work[1], &c__1);
/* Computing MIN */
    i__1 = *l, i__2 = *m - *k;
    ibnd = f2cmin(i__1,i__2);
    i__1 = ibnd;
    for (i__ = 1; i__ <= i__1; ++i__) {

/*        Scan for largest ALPHA(K+I) */

	isub = i__;
	smax = work[*k + i__];
	i__2 = ibnd;
	for (j = i__ + 1; j <= i__2; ++j) {
	    temp = work[*k + j];
	    if (temp > smax) {
		isub = j;
		smax = temp;
	    }
/* L10: */
	}
	if (isub != i__) {
	    work[*k + isub] = work[*k + i__];
	    work[*k + i__] = smax;
	    iwork[*k + i__] = *k + isub;
	} else {
	    iwork[*k + i__] = *k + i__;
	}
/* L20: */
    }

    work[1] = (doublereal) lwkopt;
    return;

/*     End of DGGSVD3 */

} /* dggsvd3_ */