text: /* f2c.h  --  Standard Fortran to C header file */
  
  /**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
  
  	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
  
  #ifndef F2C_INCLUDE
  #define F2C_INCLUDE
  
  #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;
  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;}
  #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)); }
  #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  #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) = conj(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) (cimag(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;
  }
  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;
  }
  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;
  }
  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;
  	_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;
  }
  static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  	integer n = *n_, incx = *incx_, incy = *incy_, i;
  	_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;
  }	
  static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  	integer n = *n_, incx = *incx_, incy = *incy_, i;
  	_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;
  }
  static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  	integer n = *n_, incx = *incx_, incy = *incy_, i;
  	_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 real c_b3 = 0.f;
  static integer c__1 = 1;
  static real c_b40 = -1.f;
  static real c_b43 = 1.f;
  
  /* > \brief \b CTGSJA */
  
  /*  =========== DOCUMENTATION =========== */
  
  /* Online html documentation available at */
  /*            http://www.netlib.org/lapack/explore-html/ */
  
  /* > \htmlonly */
  /* > Download CTGSJA + dependencies */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctgsja.
  f"> */
  /* > [TGZ]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctgsja.
  f"> */
  /* > [ZIP]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctgsja.
  f"> */
  /* > [TXT]</a> */
  /* > \endhtmlonly */
  
  /*  Definition: */
  /*  =========== */
  
  /*       SUBROUTINE CTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B, */
  /*                          LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV, */
  /*                          Q, LDQ, WORK, NCALL MYCYCLE, INFO ) */
  
  /*       CHARACTER          JOBQ, JOBU, JOBV */
  /*       INTEGER            INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, */
  /*      $                   NCALL MYCYCLE, P */
  /*       REAL               TOLA, TOLB */
  /*       REAL               ALPHA( * ), BETA( * ) */
  /*       COMPLEX            A( LDA, * ), B( LDB, * ), Q( LDQ, * ), */
  /*      $                   U( LDU, * ), V( LDV, * ), WORK( * ) */
  
  
  /* > \par Purpose: */
  /*  ============= */
  /* > */
  /* > \verbatim */
  /* > */
  /* > CTGSJA computes the generalized singular value decomposition (GSVD) */
  /* > of two complex upper triangular (or trapezoidal) matrices A and B. */
  /* > */
  /* > On entry, it is assumed that matrices A and B have the following */
  /* > forms, which may be obtained by the preprocessing subroutine CGGSVP */
  /* > from a general M-by-N matrix A and P-by-N matrix B: */
  /* > */
  /* >              N-K-L  K    L */
  /* >    A =    K ( 0    A12  A13 ) if M-K-L >= 0; */
  /* >           L ( 0     0   A23 ) */
  /* >       M-K-L ( 0     0    0  ) */
  /* > */
  /* >            N-K-L  K    L */
  /* >    A =  K ( 0    A12  A13 ) if M-K-L < 0; */
  /* >       M-K ( 0     0   A23 ) */
  /* > */
  /* >            N-K-L  K    L */
  /* >    B =  L ( 0     0   B13 ) */
  /* >       P-L ( 0     0    0  ) */
  /* > */
  /* > where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular */
  /* > upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, */
  /* > otherwise A23 is (M-K)-by-L upper trapezoidal. */
  /* > */
  /* > On exit, */
  /* > */
  /* >        U**H *A*Q = D1*( 0 R ),    V**H *B*Q = D2*( 0 R ), */
  /* > */
  /* > where U, V and Q are unitary matrices. */
  /* > R is a nonsingular upper triangular matrix, and D1 */
  /* > and D2 are ``diagonal'' matrices, which are of the following */
  /* > structures: */
  /* > */
  /* > 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 ) K */
  /* >             L (  0    0   R22 ) L */
  /* > */
  /* > 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. */
  /* > */
  /* > R = ( 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 computation of the unitary transformation matrices U, V or Q */
  /* > is optional.  These matrices may either be formed explicitly, or they */
  /* > may be postmultiplied into input matrices U1, V1, or Q1. */
  /* > \endverbatim */
  
  /*  Arguments: */
  /*  ========== */
  
  /* > \param[in] JOBU */
  /* > \verbatim */
  /* >          JOBU is CHARACTER*1 */
  /* >          = 'U':  U must contain a unitary matrix U1 on entry, and */
  /* >                  the product U1*U is returned; */
  /* >          = 'I':  U is initialized to the unit matrix, and the */
  /* >                  unitary matrix U is returned; */
  /* >          = 'N':  U is not computed. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] JOBV */
  /* > \verbatim */
  /* >          JOBV is CHARACTER*1 */
  /* >          = 'V':  V must contain a unitary matrix V1 on entry, and */
  /* >                  the product V1*V is returned; */
  /* >          = 'I':  V is initialized to the unit matrix, and the */
  /* >                  unitary matrix V is returned; */
  /* >          = 'N':  V is not computed. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] JOBQ */
  /* > \verbatim */
  /* >          JOBQ is CHARACTER*1 */
  /* >          = 'Q':  Q must contain a unitary matrix Q1 on entry, and */
  /* >                  the product Q1*Q is returned; */
  /* >          = 'I':  Q is initialized to the unit matrix, and the */
  /* >                  unitary matrix Q is returned; */
  /* >          = '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] P */
  /* > \verbatim */
  /* >          P is INTEGER */
  /* >          The number of rows of the matrix B.  P >= 0. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] N */
  /* > \verbatim */
  /* >          N is INTEGER */
  /* >          The number of columns of the matrices A and B.  N >= 0. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] K */
  /* > \verbatim */
  /* >          K is INTEGER */
  /* > \endverbatim */
  /* > */
  /* > \param[in] L */
  /* > \verbatim */
  /* >          L is INTEGER */
  /* > */
  /* >          K and L specify the subblocks in the input matrices A and B: */
  /* >          A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,,N-L+1:N) */
  /* >          of A and B, whose GSVD is going to be computed by CTGSJA. */
  /* >          See Further Details. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] A */
  /* > \verbatim */
  /* >          A is COMPLEX array, dimension (LDA,N) */
  /* >          On entry, the M-by-N matrix A. */
  /* >          On exit, A(N-K+1:N,1:MIN(K+L,M) ) 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 COMPLEX array, dimension (LDB,N) */
  /* >          On entry, the P-by-N matrix B. */
  /* >          On exit, if necessary, B(M-K+1:L,N+M-K-L+1:N) contains */
  /* >          a part of R.  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[in] TOLA */
  /* > \verbatim */
  /* >          TOLA is REAL */
  /* > \endverbatim */
  /* > */
  /* > \param[in] TOLB */
  /* > \verbatim */
  /* >          TOLB is REAL */
  /* > */
  /* >          TOLA and TOLB are the convergence criteria for the Jacobi- */
  /* >          Kogbetliantz iteration procedure. Generally, they are the */
  /* >          same as used in the preprocessing step, say */
  /* >              TOLA = MAX(M,N)*norm(A)*MACHEPS, */
  /* >              TOLB = MAX(P,N)*norm(B)*MACHEPS. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] ALPHA */
  /* > \verbatim */
  /* >          ALPHA is REAL array, dimension (N) */
  /* > \endverbatim */
  /* > */
  /* > \param[out] BETA */
  /* > \verbatim */
  /* >          BETA is REAL 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) = diag(C), */
  /* >            BETA(K+1:K+L)  = diag(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. */
  /* >          Furthermore, if K+L < N, */
  /* >            ALPHA(K+L+1:N) = 0 */
  /* >            BETA(K+L+1:N)  = 0. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] U */
  /* > \verbatim */
  /* >          U is COMPLEX array, dimension (LDU,M) */
  /* >          On entry, if JOBU = 'U', U must contain a matrix U1 (usually */
  /* >          the unitary matrix returned by CGGSVP). */
  /* >          On exit, */
  /* >          if JOBU = 'I', U contains the unitary matrix U; */
  /* >          if JOBU = 'U', U contains the product U1*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[in,out] V */
  /* > \verbatim */
  /* >          V is COMPLEX array, dimension (LDV,P) */
  /* >          On entry, if JOBV = 'V', V must contain a matrix V1 (usually */
  /* >          the unitary matrix returned by CGGSVP). */
  /* >          On exit, */
  /* >          if JOBV = 'I', V contains the unitary matrix V; */
  /* >          if JOBV = 'V', V contains the product V1*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[in,out] Q */
  /* > \verbatim */
  /* >          Q is COMPLEX array, dimension (LDQ,N) */
  /* >          On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually */
  /* >          the unitary matrix returned by CGGSVP). */
  /* >          On exit, */
  /* >          if JOBQ = 'I', Q contains the unitary matrix Q; */
  /* >          if JOBQ = 'Q', Q contains the product Q1*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 COMPLEX array, dimension (2*N) */
  /* > \endverbatim */
  /* > */
  /* > \param[out] NCALL MYCYCLE */
  /* > \verbatim */
  /* >          NCALL MYCYCLE is INTEGER */
  /* >          The number of cycles required for convergence. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] INFO */
  /* > \verbatim */
  /* >          INFO is INTEGER */
  /* >          = 0:  successful exit */
  /* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
  /* >          = 1:  the procedure does not converge after MAXIT cycles. */
  /* > \endverbatim */
  
  /* > \par Internal Parameters: */
  /*  ========================= */
  /* > */
  /* > \verbatim */
  /* >  MAXIT   INTEGER */
  /* >          MAXIT specifies the total loops that the iterative procedure */
  /* >          may take. If after MAXIT cycles, the routine fails to */
  /* >          converge, we return INFO = 1. */
  /* > \endverbatim */
  
  /*  Authors: */
  /*  ======== */
  
  /* > \author Univ. of Tennessee */
  /* > \author Univ. of California Berkeley */
  /* > \author Univ. of Colorado Denver */
  /* > \author NAG Ltd. */
  
  /* > \date December 2016 */
  
  /* > \ingroup complexOTHERcomputational */
  
  /* > \par Further Details: */
  /*  ===================== */
  /* > */
  /* > \verbatim */
  /* > */
  /* >  CTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce */
  /* >  f2cmin(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L */
  /* >  matrix B13 to the form: */
  /* > */
  /* >           U1**H *A13*Q1 = C1*R1; V1**H *B13*Q1 = S1*R1, */
  /* > */
  /* >  where U1, V1 and Q1 are unitary matrix. */
  /* >  C1 and S1 are diagonal matrices satisfying */
  /* > */
  /* >                C1**2 + S1**2 = I, */
  /* > */
  /* >  and R1 is an L-by-L nonsingular upper triangular matrix. */
  /* > \endverbatim */
  /* > */
  /*  ===================================================================== */
  /* Subroutine */ int ctgsja_(char *jobu, char *jobv, char *jobq, integer *m, 
  	integer *p, integer *n, integer *k, integer *l, complex *a, integer *
  	lda, complex *b, integer *ldb, real *tola, real *tolb, real *alpha, 
  	real *beta, complex *u, integer *ldu, complex *v, integer *ldv, 
  	complex *q, integer *ldq, complex *work, integer *ncallmycycle, 
  	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, i__3, i__4;
      real r__1;
      complex q__1;
  
      /* Local variables */
      extern /* Subroutine */ int crot_(integer *, complex *, integer *, 
  	    complex *, integer *, real *, complex *);
      integer kcallmycycle, i__, j;
      real gamma;
      extern logical lsame_(char *, char *);
      extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
  	    complex *, integer *);
      logical initq;
      real a1, a3, b1;
      logical initu, initv, wantq, upper;
      real b3, error;
      logical wantu, wantv;
      real ssmin;
      complex a2, b2;
      extern /* Subroutine */ int clags2_(logical *, real *, complex *, real *, 
  	    real *, complex *, real *, real *, complex *, real *, complex *, 
  	    real *, complex *), clapll_(integer *, complex *, integer *, 
  	    complex *, integer *, real *), csscal_(integer *, real *, complex 
  	    *, integer *), claset_(char *, integer *, integer *, complex *, 
  	    complex *, complex *, integer *), xerbla_(char *, integer 
  	    *, ftnlen), slartg_(real *, real *, real *, real *, real *);
  //    extern integer myhuge_(real *);
      real csq, csu, csv;
      complex snq;
      real rwk;
      complex snu, snv;
  
  
  /*  -- LAPACK computational routine (version 3.7.0) -- */
  /*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
  /*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  /*     December 2016 */
  
  
  /*  ===================================================================== */
  
  
  
  /*     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;
  
      /* Function Body */
      initu = lsame_(jobu, "I");
      wantu = initu || lsame_(jobu, "U");
  
      initv = lsame_(jobv, "I");
      wantv = initv || lsame_(jobv, "V");
  
      initq = lsame_(jobq, "I");
      wantq = initq || lsame_(jobq, "Q");
  
      *info = 0;
      if (! (initu || wantu || lsame_(jobu, "N"))) {
  	*info = -1;
      } else if (! (initv || wantv || lsame_(jobv, "N"))) 
  	    {
  	*info = -2;
      } else if (! (initq || wantq || lsame_(jobq, "N"))) 
  	    {
  	*info = -3;
      } else if (*m < 0) {
  	*info = -4;
      } else if (*p < 0) {
  	*info = -5;
      } else if (*n < 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 = -18;
      } else if (*ldv < 1 || wantv && *ldv < *p) {
  	*info = -20;
      } else if (*ldq < 1 || wantq && *ldq < *n) {
  	*info = -22;
      }
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("CTGSJA", &i__1, (ftnlen)6);
  	return 0;
      }
  
  /*     Initialize U, V and Q, if necessary */
  
      if (initu) {
  	claset_("Full", m, m, &c_b1, &c_b2, &u[u_offset], ldu);
      }
      if (initv) {
  	claset_("Full", p, p, &c_b1, &c_b2, &v[v_offset], ldv);
      }
      if (initq) {
  	claset_("Full", n, n, &c_b1, &c_b2, &q[q_offset], ldq);
      }
  
  /*     Loop until convergence */
  
      upper = FALSE_;
      for (kcallmycycle = 1; kcallmycycle <= 40; ++kcallmycycle) {
  
  	upper = ! upper;
  
  	i__1 = *l - 1;
  	for (i__ = 1; i__ <= i__1; ++i__) {
  	    i__2 = *l;
  	    for (j = i__ + 1; j <= i__2; ++j) {
  
  		a1 = 0.f;
  		a2.r = 0.f, a2.i = 0.f;
  		a3 = 0.f;
  		if (*k + i__ <= *m) {
  		    i__3 = *k + i__ + (*n - *l + i__) * a_dim1;
  		    a1 = a[i__3].r;
  		}
  		if (*k + j <= *m) {
  		    i__3 = *k + j + (*n - *l + j) * a_dim1;
  		    a3 = a[i__3].r;
  		}
  
  		i__3 = i__ + (*n - *l + i__) * b_dim1;
  		b1 = b[i__3].r;
  		i__3 = j + (*n - *l + j) * b_dim1;
  		b3 = b[i__3].r;
  
  		if (upper) {
  		    if (*k + i__ <= *m) {
  			i__3 = *k + i__ + (*n - *l + j) * a_dim1;
  			a2.r = a[i__3].r, a2.i = a[i__3].i;
  		    }
  		    i__3 = i__ + (*n - *l + j) * b_dim1;
  		    b2.r = b[i__3].r, b2.i = b[i__3].i;
  		} else {
  		    if (*k + j <= *m) {
  			i__3 = *k + j + (*n - *l + i__) * a_dim1;
  			a2.r = a[i__3].r, a2.i = a[i__3].i;
  		    }
  		    i__3 = j + (*n - *l + i__) * b_dim1;
  		    b2.r = b[i__3].r, b2.i = b[i__3].i;
  		}
  
  		clags2_(&upper, &a1, &a2, &a3, &b1, &b2, &b3, &csu, &snu, &
  			csv, &snv, &csq, &snq);
  
  /*              Update (K+I)-th and (K+J)-th rows of matrix A: U**H *A */
  
  		if (*k + j <= *m) {
  		    r_cnjg(&q__1, &snu);
  		    crot_(l, &a[*k + j + (*n - *l + 1) * a_dim1], lda, &a[*k 
  			    + i__ + (*n - *l + 1) * a_dim1], lda, &csu, &q__1)
  			    ;
  		}
  
  /*              Update I-th and J-th rows of matrix B: V**H *B */
  
  		r_cnjg(&q__1, &snv);
  		crot_(l, &b[j + (*n - *l + 1) * b_dim1], ldb, &b[i__ + (*n - *
  			l + 1) * b_dim1], ldb, &csv, &q__1);
  
  /*              Update (N-L+I)-th and (N-L+J)-th columns of matrices */
  /*              A and B: A*Q and B*Q */
  
  /* Computing MIN */
  		i__4 = *k + *l;
  		i__3 = f2cmin(i__4,*m);
  		crot_(&i__3, &a[(*n - *l + j) * a_dim1 + 1], &c__1, &a[(*n - *
  			l + i__) * a_dim1 + 1], &c__1, &csq, &snq);
  
  		crot_(l, &b[(*n - *l + j) * b_dim1 + 1], &c__1, &b[(*n - *l + 
  			i__) * b_dim1 + 1], &c__1, &csq, &snq);
  
  		if (upper) {
  		    if (*k + i__ <= *m) {
  			i__3 = *k + i__ + (*n - *l + j) * a_dim1;
  			a[i__3].r = 0.f, a[i__3].i = 0.f;
  		    }
  		    i__3 = i__ + (*n - *l + j) * b_dim1;
  		    b[i__3].r = 0.f, b[i__3].i = 0.f;
  		} else {
  		    if (*k + j <= *m) {
  			i__3 = *k + j + (*n - *l + i__) * a_dim1;
  			a[i__3].r = 0.f, a[i__3].i = 0.f;
  		    }
  		    i__3 = j + (*n - *l + i__) * b_dim1;
  		    b[i__3].r = 0.f, b[i__3].i = 0.f;
  		}
  
  /*              Ensure that the diagonal elements of A and B are real. */
  
  		if (*k + i__ <= *m) {
  		    i__3 = *k + i__ + (*n - *l + i__) * a_dim1;
  		    i__4 = *k + i__ + (*n - *l + i__) * a_dim1;
  		    r__1 = a[i__4].r;
  		    a[i__3].r = r__1, a[i__3].i = 0.f;
  		}
  		if (*k + j <= *m) {
  		    i__3 = *k + j + (*n - *l + j) * a_dim1;
  		    i__4 = *k + j + (*n - *l + j) * a_dim1;
  		    r__1 = a[i__4].r;
  		    a[i__3].r = r__1, a[i__3].i = 0.f;
  		}
  		i__3 = i__ + (*n - *l + i__) * b_dim1;
  		i__4 = i__ + (*n - *l + i__) * b_dim1;
  		r__1 = b[i__4].r;
  		b[i__3].r = r__1, b[i__3].i = 0.f;
  		i__3 = j + (*n - *l + j) * b_dim1;
  		i__4 = j + (*n - *l + j) * b_dim1;
  		r__1 = b[i__4].r;
  		b[i__3].r = r__1, b[i__3].i = 0.f;
  
  /*              Update unitary matrices U, V, Q, if desired. */
  
  		if (wantu && *k + j <= *m) {
  		    crot_(m, &u[(*k + j) * u_dim1 + 1], &c__1, &u[(*k + i__) *
  			     u_dim1 + 1], &c__1, &csu, &snu);
  		}
  
  		if (wantv) {
  		    crot_(p, &v[j * v_dim1 + 1], &c__1, &v[i__ * v_dim1 + 1], 
  			    &c__1, &csv, &snv);
  		}
  
  		if (wantq) {
  		    crot_(n, &q[(*n - *l + j) * q_dim1 + 1], &c__1, &q[(*n - *
  			    l + i__) * q_dim1 + 1], &c__1, &csq, &snq);
  		}
  
  /* L10: */
  	    }
  /* L20: */
  	}
  
  	if (! upper) {
  
  /*           The matrices A13 and B13 were lower triangular at the start */
  /*           of the cycle, and are now upper triangular. */
  
  /*           Convergence test: test the parallelism of the corresponding */
  /*           rows of A and B. */
  
  	    error = 0.f;
  /* Computing MIN */
  	    i__2 = *l, i__3 = *m - *k;
  	    i__1 = f2cmin(i__2,i__3);
  	    for (i__ = 1; i__ <= i__1; ++i__) {
  		i__2 = *l - i__ + 1;
  		ccopy_(&i__2, &a[*k + i__ + (*n - *l + i__) * a_dim1], lda, &
  			work[1], &c__1);
  		i__2 = *l - i__ + 1;
  		ccopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &work[*
  			l + 1], &c__1);
  		i__2 = *l - i__ + 1;
  		clapll_(&i__2, &work[1], &c__1, &work[*l + 1], &c__1, &ssmin);
  		error = f2cmax(error,ssmin);
  /* L30: */
  	    }
  
  	    if (abs(error) <= f2cmin(*tola,*tolb)) {
  		goto L50;
  	    }
  	}
  
  /*        End of cycle loop */
  
  /* L40: */
      }
  
  /*     The algorithm has not converged after MAXIT cycles. */
  
      *info = 1;
      goto L100;
  
  L50:
  
  /*     If ERROR <= MIN(TOLA,TOLB), then the algorithm has converged. */
  /*     Compute the generalized singular value pairs (ALPHA, BETA), and */
  /*     set the triangular matrix R to array A. */
  
      i__1 = *k;
      for (i__ = 1; i__ <= i__1; ++i__) {
  	alpha[i__] = 1.f;
  	beta[i__] = 0.f;
  /* L60: */
      }
  
  /* Computing MIN */
      i__2 = *l, i__3 = *m - *k;
      i__1 = f2cmin(i__2,i__3);
      for (i__ = 1; i__ <= i__1; ++i__) {
  
  	i__2 = *k + i__ + (*n - *l + i__) * a_dim1;
  	a1 = a[i__2].r;
  	i__2 = i__ + (*n - *l + i__) * b_dim1;
  	b1 = b[i__2].r;
  	gamma = b1 / a1;
  
  	if (gamma <= (real) myhuge_(&c_b3) && gamma >= -((real) myhuge_(&c_b3)
  		)) {
  
  	    if (gamma < 0.f) {
  		i__2 = *l - i__ + 1;
  		csscal_(&i__2, &c_b40, &b[i__ + (*n - *l + i__) * b_dim1], 
  			ldb);
  		if (wantv) {
  		    csscal_(p, &c_b40, &v[i__ * v_dim1 + 1], &c__1);
  		}
  	    }
  
  	    r__1 = abs(gamma);
  	    slartg_(&r__1, &c_b43, &beta[*k + i__], &alpha[*k + i__], &rwk);
  
  	    if (alpha[*k + i__] >= beta[*k + i__]) {
  		i__2 = *l - i__ + 1;
  		r__1 = 1.f / alpha[*k + i__];
  		csscal_(&i__2, &r__1, &a[*k + i__ + (*n - *l + i__) * a_dim1],
  			 lda);
  	    } else {
  		i__2 = *l - i__ + 1;
  		r__1 = 1.f / beta[*k + i__];
  		csscal_(&i__2, &r__1, &b[i__ + (*n - *l + i__) * b_dim1], ldb)
  			;
  		i__2 = *l - i__ + 1;
  		ccopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k 
  			+ i__ + (*n - *l + i__) * a_dim1], lda);
  	    }
  
  	} else {
  	    alpha[*k + i__] = 0.f;
  	    beta[*k + i__] = 1.f;
  	    i__2 = *l - i__ + 1;
  	    ccopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k + 
  		    i__ + (*n - *l + i__) * a_dim1], lda);
  	}
  /* L70: */
      }
  
  /*     Post-assignment */
  
      i__1 = *k + *l;
      for (i__ = *m + 1; i__ <= i__1; ++i__) {
  	alpha[i__] = 0.f;
  	beta[i__] = 1.f;
  /* L80: */
      }
  
      if (*k + *l < *n) {
  	i__1 = *n;
  	for (i__ = *k + *l + 1; i__ <= i__1; ++i__) {
  	    alpha[i__] = 0.f;
  	    beta[i__] = 0.f;
  /* L90: */
  	}
      }
  
  L100:
      *ncallmycycle = kcallmycycle;
  
      return 0;
  
  /*     End of CTGSJA */
  
  } /* ctgsja_ */
  
  