text: #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__0 = 0;
  static real c_b7 = 1.f;
  static integer c__1 = 1;
  static integer c_n1 = -1;
  
  /* > \brief \b SLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller o
  nes by appending a row. Used by sbdsdc. */
  
  /*  =========== DOCUMENTATION =========== */
  
  /* Online html documentation available at */
  /*            http://www.netlib.org/lapack/explore-html/ */
  
  /* > \htmlonly */
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  /*  Definition: */
  /*  =========== */
  
  /*       SUBROUTINE SLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA, */
  /*                          IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, */
  /*                          LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, */
  /*                          IWORK, INFO ) */
  
  /*       INTEGER            GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, */
  /*      $                   NR, SQRE */
  /*       REAL               ALPHA, BETA, C, S */
  /*       INTEGER            GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ), */
  /*      $                   PERM( * ) */
  /*       REAL               D( * ), DIFL( * ), DIFR( * ), */
  /*      $                   GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ), */
  /*      $                   VF( * ), VL( * ), WORK( * ), Z( * ) */
  
  
  /* > \par Purpose: */
  /*  ============= */
  /* > */
  /* > \verbatim */
  /* > */
  /* > SLASD6 computes the SVD of an updated upper bidiagonal matrix B */
  /* > obtained by merging two smaller ones by appending a row. This */
  /* > routine is used only for the problem which requires all singular */
  /* > values and optionally singular vector matrices in factored form. */
  /* > B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */
  /* > A related subroutine, SLASD1, handles the case in which all singular */
  /* > values and singular vectors of the bidiagonal matrix are desired. */
  /* > */
  /* > SLASD6 computes the SVD as follows: */
  /* > */
  /* >               ( D1(in)    0    0       0 ) */
  /* >   B = U(in) * (   Z1**T   a   Z2**T    b ) * VT(in) */
  /* >               (   0       0   D2(in)   0 ) */
  /* > */
  /* >     = U(out) * ( D(out) 0) * VT(out) */
  /* > */
  /* > where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M */
  /* > with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */
  /* > elsewhere; and the entry b is empty if SQRE = 0. */
  /* > */
  /* > The singular values of B can be computed using D1, D2, the first */
  /* > components of all the right singular vectors of the lower block, and */
  /* > the last components of all the right singular vectors of the upper */
  /* > block. These components are stored and updated in VF and VL, */
  /* > respectively, in SLASD6. Hence U and VT are not explicitly */
  /* > referenced. */
  /* > */
  /* > The singular values are stored in D. The algorithm consists of two */
  /* > stages: */
  /* > */
  /* >       The first stage consists of deflating the size of the problem */
  /* >       when there are multiple singular values or if there is a zero */
  /* >       in the Z vector. For each such occurrence the dimension of the */
  /* >       secular equation problem is reduced by one. This stage is */
  /* >       performed by the routine SLASD7. */
  /* > */
  /* >       The second stage consists of calculating the updated */
  /* >       singular values. This is done by finding the roots of the */
  /* >       secular equation via the routine SLASD4 (as called by SLASD8). */
  /* >       This routine also updates VF and VL and computes the distances */
  /* >       between the updated singular values and the old singular */
  /* >       values. */
  /* > */
  /* > SLASD6 is called from SLASDA. */
  /* > \endverbatim */
  
  /*  Arguments: */
  /*  ========== */
  
  /* > \param[in] ICOMPQ */
  /* > \verbatim */
  /* >          ICOMPQ is INTEGER */
  /* >         Specifies whether singular vectors are to be computed in */
  /* >         factored form: */
  /* >         = 0: Compute singular values only. */
  /* >         = 1: Compute singular vectors in factored form as well. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] NL */
  /* > \verbatim */
  /* >          NL is INTEGER */
  /* >         The row dimension of the upper block.  NL >= 1. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] NR */
  /* > \verbatim */
  /* >          NR is INTEGER */
  /* >         The row dimension of the lower block.  NR >= 1. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] SQRE */
  /* > \verbatim */
  /* >          SQRE is INTEGER */
  /* >         = 0: the lower block is an NR-by-NR square matrix. */
  /* >         = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */
  /* > */
  /* >         The bidiagonal matrix has row dimension N = NL + NR + 1, */
  /* >         and column dimension M = N + SQRE. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] D */
  /* > \verbatim */
  /* >          D is REAL array, dimension (NL+NR+1). */
  /* >         On entry D(1:NL,1:NL) contains the singular values of the */
  /* >         upper block, and D(NL+2:N) contains the singular values */
  /* >         of the lower block. On exit D(1:N) contains the singular */
  /* >         values of the modified matrix. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] VF */
  /* > \verbatim */
  /* >          VF is REAL array, dimension (M) */
  /* >         On entry, VF(1:NL+1) contains the first components of all */
  /* >         right singular vectors of the upper block; and VF(NL+2:M) */
  /* >         contains the first components of all right singular vectors */
  /* >         of the lower block. On exit, VF contains the first components */
  /* >         of all right singular vectors of the bidiagonal matrix. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] VL */
  /* > \verbatim */
  /* >          VL is REAL array, dimension (M) */
  /* >         On entry, VL(1:NL+1) contains the  last components of all */
  /* >         right singular vectors of the upper block; and VL(NL+2:M) */
  /* >         contains the last components of all right singular vectors of */
  /* >         the lower block. On exit, VL contains the last components of */
  /* >         all right singular vectors of the bidiagonal matrix. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] ALPHA */
  /* > \verbatim */
  /* >          ALPHA is REAL */
  /* >         Contains the diagonal element associated with the added row. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] BETA */
  /* > \verbatim */
  /* >          BETA is REAL */
  /* >         Contains the off-diagonal element associated with the added */
  /* >         row. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] IDXQ */
  /* > \verbatim */
  /* >          IDXQ is INTEGER array, dimension (N) */
  /* >         This contains the permutation which will reintegrate the */
  /* >         subproblem just solved back into sorted order, i.e. */
  /* >         D( IDXQ( I = 1, N ) ) will be in ascending order. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] PERM */
  /* > \verbatim */
  /* >          PERM is INTEGER array, dimension ( N ) */
  /* >         The permutations (from deflation and sorting) to be applied */
  /* >         to each block. Not referenced if ICOMPQ = 0. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] GIVPTR */
  /* > \verbatim */
  /* >          GIVPTR is INTEGER */
  /* >         The number of Givens rotations which took place in this */
  /* >         subproblem. Not referenced if ICOMPQ = 0. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] GIVCOL */
  /* > \verbatim */
  /* >          GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */
  /* >         Each pair of numbers indicates a pair of columns to take place */
  /* >         in a Givens rotation. Not referenced if ICOMPQ = 0. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LDGCOL */
  /* > \verbatim */
  /* >          LDGCOL is INTEGER */
  /* >         leading dimension of GIVCOL, must be at least N. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] GIVNUM */
  /* > \verbatim */
  /* >          GIVNUM is REAL array, dimension ( LDGNUM, 2 ) */
  /* >         Each number indicates the C or S value to be used in the */
  /* >         corresponding Givens rotation. Not referenced if ICOMPQ = 0. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LDGNUM */
  /* > \verbatim */
  /* >          LDGNUM is INTEGER */
  /* >         The leading dimension of GIVNUM and POLES, must be at least N. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] POLES */
  /* > \verbatim */
  /* >          POLES is REAL array, dimension ( LDGNUM, 2 ) */
  /* >         On exit, POLES(1,*) is an array containing the new singular */
  /* >         values obtained from solving the secular equation, and */
  /* >         POLES(2,*) is an array containing the poles in the secular */
  /* >         equation. Not referenced if ICOMPQ = 0. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] DIFL */
  /* > \verbatim */
  /* >          DIFL is REAL array, dimension ( N ) */
  /* >         On exit, DIFL(I) is the distance between I-th updated */
  /* >         (undeflated) singular value and the I-th (undeflated) old */
  /* >         singular value. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] DIFR */
  /* > \verbatim */
  /* >          DIFR is REAL array, */
  /* >                   dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and */
  /* >                   dimension ( K ) if ICOMPQ = 0. */
  /* >          On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not */
  /* >          defined and will not be referenced. */
  /* > */
  /* >          If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */
  /* >          normalizing factors for the right singular vector matrix. */
  /* > */
  /* >         See SLASD8 for details on DIFL and DIFR. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] Z */
  /* > \verbatim */
  /* >          Z is REAL array, dimension ( M ) */
  /* >         The first elements of this array contain the components */
  /* >         of the deflation-adjusted updating row vector. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] K */
  /* > \verbatim */
  /* >          K is INTEGER */
  /* >         Contains the dimension of the non-deflated matrix, */
  /* >         This is the order of the related secular equation. 1 <= K <=N. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] C */
  /* > \verbatim */
  /* >          C is REAL */
  /* >         C contains garbage if SQRE =0 and the C-value of a Givens */
  /* >         rotation related to the right null space if SQRE = 1. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] S */
  /* > \verbatim */
  /* >          S is REAL */
  /* >         S contains garbage if SQRE =0 and the S-value of a Givens */
  /* >         rotation related to the right null space if SQRE = 1. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] WORK */
  /* > \verbatim */
  /* >          WORK is REAL array, dimension ( 4 * M ) */
  /* > \endverbatim */
  /* > */
  /* > \param[out] IWORK */
  /* > \verbatim */
  /* >          IWORK is INTEGER array, dimension ( 3 * 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, a singular value did not converge */
  /* > \endverbatim */
  
  /*  Authors: */
  /*  ======== */
  
  /* > \author Univ. of Tennessee */
  /* > \author Univ. of California Berkeley */
  /* > \author Univ. of Colorado Denver */
  /* > \author NAG Ltd. */
  
  /* > \date June 2016 */
  
  /* > \ingroup OTHERauxiliary */
  
  /* > \par Contributors: */
  /*  ================== */
  /* > */
  /* >     Ming Gu and Huan Ren, Computer Science Division, University of */
  /* >     California at Berkeley, USA */
  /* > */
  /*  ===================================================================== */
  /* Subroutine */ int slasd6_(integer *icompq, integer *nl, integer *nr, 
  	integer *sqre, real *d__, real *vf, real *vl, real *alpha, real *beta,
  	 integer *idxq, integer *perm, integer *givptr, integer *givcol, 
  	integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real *
  	difl, real *difr, real *z__, integer *k, real *c__, real *s, real *
  	work, integer *iwork, integer *info)
  {
      /* System generated locals */
      integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, 
  	    poles_dim1, poles_offset, i__1;
      real r__1, r__2;
  
      /* Local variables */
      integer idxc, idxp, ivfw, ivlw, i__, m, n;
      extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
  	    integer *);
      integer n1, n2;
      extern /* Subroutine */ int slasd7_(integer *, integer *, integer *, 
  	    integer *, integer *, real *, real *, real *, real *, real *, 
  	    real *, real *, real *, real *, real *, integer *, integer *, 
  	    integer *, integer *, integer *, integer *, integer *, real *, 
  	    integer *, real *, real *, integer *), slasd8_(integer *, integer 
  	    *, real *, real *, real *, real *, real *, real *, integer *, 
  	    real *, real *, integer *);
      integer iw, isigma;
      extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), slascl_(
  	    char *, integer *, integer *, real *, real *, integer *, integer *
  	    , real *, integer *, integer *), slamrg_(integer *, 
  	    integer *, real *, integer *, integer *, integer *);
      real orgnrm;
      integer idx;
  
  
  /*  -- 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 */
  
  
  /*  ===================================================================== */
  
  
  /*     Test the input parameters. */
  
      /* Parameter adjustments */
      --d__;
      --vf;
      --vl;
      --idxq;
      --perm;
      givcol_dim1 = *ldgcol;
      givcol_offset = 1 + givcol_dim1 * 1;
      givcol -= givcol_offset;
      poles_dim1 = *ldgnum;
      poles_offset = 1 + poles_dim1 * 1;
      poles -= poles_offset;
      givnum_dim1 = *ldgnum;
      givnum_offset = 1 + givnum_dim1 * 1;
      givnum -= givnum_offset;
      --difl;
      --difr;
      --z__;
      --work;
      --iwork;
  
      /* Function Body */
      *info = 0;
      n = *nl + *nr + 1;
      m = n + *sqre;
  
      if (*icompq < 0 || *icompq > 1) {
  	*info = -1;
      } else if (*nl < 1) {
  	*info = -2;
      } else if (*nr < 1) {
  	*info = -3;
      } else if (*sqre < 0 || *sqre > 1) {
  	*info = -4;
      } else if (*ldgcol < n) {
  	*info = -14;
      } else if (*ldgnum < n) {
  	*info = -16;
      }
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("SLASD6", &i__1, (ftnlen)6);
  	return 0;
      }
  
  /*     The following values are for bookkeeping purposes only.  They are */
  /*     integer pointers which indicate the portion of the workspace */
  /*     used by a particular array in SLASD7 and SLASD8. */
  
      isigma = 1;
      iw = isigma + n;
      ivfw = iw + m;
      ivlw = ivfw + m;
  
      idx = 1;
      idxc = idx + n;
      idxp = idxc + n;
  
  /*     Scale. */
  
  /* Computing MAX */
      r__1 = abs(*alpha), r__2 = abs(*beta);
      orgnrm = f2cmax(r__1,r__2);
      d__[*nl + 1] = 0.f;
      i__1 = n;
      for (i__ = 1; i__ <= i__1; ++i__) {
  	if ((r__1 = d__[i__], abs(r__1)) > orgnrm) {
  	    orgnrm = (r__1 = d__[i__], abs(r__1));
  	}
  /* L10: */
      }
      slascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info);
      *alpha /= orgnrm;
      *beta /= orgnrm;
  
  /*     Sort and Deflate singular values. */
  
      slasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], &
  	    work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], &
  	    iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[
  	    givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s, 
  	    info);
  
  /*     Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */
  
      slasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1], 
  	    ldgnum, &work[isigma], &work[iw], info);
  
  /*     Report the possible convergence failure. */
  
      if (*info != 0) {
  	return 0;
      }
  
  /*     Save the poles if ICOMPQ = 1. */
  
      if (*icompq == 1) {
  	scopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1);
  	scopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1);
      }
  
  /*     Unscale. */
  
      slascl_("G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info);
  
  /*     Prepare the IDXQ sorting permutation. */
  
      n1 = *k;
      n2 = n - *k;
      slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]);
  
      return 0;
  
  /*     End of SLASD6 */
  
  } /* slasd6_ */
  
  