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 doublereal c_b4 = -1.;
  static doublereal c_b5 = 1.;
  static integer c__1 = 1;
  static doublereal c_b16 = 0.;
  
  /* > \brief \b DLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. */
  
  /*  =========== DOCUMENTATION =========== */
  
  /* Online html documentation available at */
  /*            http://www.netlib.org/lapack/explore-html/ */
  
  /* > \htmlonly */
  /* > Download DLABRD + dependencies */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlabrd.
  f"> */
  /* > [TGZ]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlabrd.
  f"> */
  /* > [ZIP]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlabrd.
  f"> */
  /* > [TXT]</a> */
  /* > \endhtmlonly */
  
  /*  Definition: */
  /*  =========== */
  
  /*       SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, */
  /*                          LDY ) */
  
  /*       INTEGER            LDA, LDX, LDY, M, N, NB */
  /*       DOUBLE PRECISION   A( LDA, * ), D( * ), E( * ), TAUP( * ), */
  /*      $                   TAUQ( * ), X( LDX, * ), Y( LDY, * ) */
  
  
  /* > \par Purpose: */
  /*  ============= */
  /* > */
  /* > \verbatim */
  /* > */
  /* > DLABRD reduces the first NB rows and columns of a real general */
  /* > m by n matrix A to upper or lower bidiagonal form by an orthogonal */
  /* > transformation Q**T * A * P, and returns the matrices X and Y which */
  /* > are needed to apply the transformation to the unreduced part of A. */
  /* > */
  /* > If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower */
  /* > bidiagonal form. */
  /* > */
  /* > This is an auxiliary routine called by DGEBRD */
  /* > \endverbatim */
  
  /*  Arguments: */
  /*  ========== */
  
  /* > \param[in] M */
  /* > \verbatim */
  /* >          M is INTEGER */
  /* >          The number of rows in the matrix A. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] N */
  /* > \verbatim */
  /* >          N is INTEGER */
  /* >          The number of columns in the matrix A. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] NB */
  /* > \verbatim */
  /* >          NB is INTEGER */
  /* >          The number of leading rows and columns of A to be reduced. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] A */
  /* > \verbatim */
  /* >          A is DOUBLE PRECISION array, dimension (LDA,N) */
  /* >          On entry, the m by n general matrix to be reduced. */
  /* >          On exit, the first NB rows and columns of the matrix are */
  /* >          overwritten; the rest of the array is unchanged. */
  /* >          If m >= n, elements on and below the diagonal in the first NB */
  /* >            columns, with the array TAUQ, represent the orthogonal */
  /* >            matrix Q as a product of elementary reflectors; and */
  /* >            elements above the diagonal in the first NB rows, with the */
  /* >            array TAUP, represent the orthogonal matrix P as a product */
  /* >            of elementary reflectors. */
  /* >          If m < n, elements below the diagonal in the first NB */
  /* >            columns, with the array TAUQ, represent the orthogonal */
  /* >            matrix Q as a product of elementary reflectors, and */
  /* >            elements on and above the diagonal in the first NB rows, */
  /* >            with the array TAUP, represent the orthogonal matrix P as */
  /* >            a product of elementary reflectors. */
  /* >          See Further Details. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LDA */
  /* > \verbatim */
  /* >          LDA is INTEGER */
  /* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
  /* > \endverbatim */
  /* > */
  /* > \param[out] D */
  /* > \verbatim */
  /* >          D is DOUBLE PRECISION array, dimension (NB) */
  /* >          The diagonal elements of the first NB rows and columns of */
  /* >          the reduced matrix.  D(i) = A(i,i). */
  /* > \endverbatim */
  /* > */
  /* > \param[out] E */
  /* > \verbatim */
  /* >          E is DOUBLE PRECISION array, dimension (NB) */
  /* >          The off-diagonal elements of the first NB rows and columns of */
  /* >          the reduced matrix. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] TAUQ */
  /* > \verbatim */
  /* >          TAUQ is DOUBLE PRECISION array, dimension (NB) */
  /* >          The scalar factors of the elementary reflectors which */
  /* >          represent the orthogonal matrix Q. See Further Details. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] TAUP */
  /* > \verbatim */
  /* >          TAUP is DOUBLE PRECISION array, dimension (NB) */
  /* >          The scalar factors of the elementary reflectors which */
  /* >          represent the orthogonal matrix P. See Further Details. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] X */
  /* > \verbatim */
  /* >          X is DOUBLE PRECISION array, dimension (LDX,NB) */
  /* >          The m-by-nb matrix X required to update the unreduced part */
  /* >          of A. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LDX */
  /* > \verbatim */
  /* >          LDX is INTEGER */
  /* >          The leading dimension of the array X. LDX >= f2cmax(1,M). */
  /* > \endverbatim */
  /* > */
  /* > \param[out] Y */
  /* > \verbatim */
  /* >          Y is DOUBLE PRECISION array, dimension (LDY,NB) */
  /* >          The n-by-nb matrix Y required to update the unreduced part */
  /* >          of A. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LDY */
  /* > \verbatim */
  /* >          LDY is INTEGER */
  /* >          The leading dimension of the array Y. LDY >= f2cmax(1,N). */
  /* > \endverbatim */
  
  /*  Authors: */
  /*  ======== */
  
  /* > \author Univ. of Tennessee */
  /* > \author Univ. of California Berkeley */
  /* > \author Univ. of Colorado Denver */
  /* > \author NAG Ltd. */
  
  /* > \date June 2017 */
  
  /* > \ingroup doubleOTHERauxiliary */
  
  /* > \par Further Details: */
  /*  ===================== */
  /* > */
  /* > \verbatim */
  /* > */
  /* >  The matrices Q and P are represented as products of elementary */
  /* >  reflectors: */
  /* > */
  /* >     Q = H(1) H(2) . . . H(nb)  and  P = G(1) G(2) . . . G(nb) */
  /* > */
  /* >  Each H(i) and G(i) has the form: */
  /* > */
  /* >     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T */
  /* > */
  /* >  where tauq and taup are real scalars, and v and u are real vectors. */
  /* > */
  /* >  If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in */
  /* >  A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in */
  /* >  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
  /* > */
  /* >  If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in */
  /* >  A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in */
  /* >  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
  /* > */
  /* >  The elements of the vectors v and u together form the m-by-nb matrix */
  /* >  V and the nb-by-n matrix U**T which are needed, with X and Y, to apply */
  /* >  the transformation to the unreduced part of the matrix, using a block */
  /* >  update of the form:  A := A - V*Y**T - X*U**T. */
  /* > */
  /* >  The contents of A on exit are illustrated by the following examples */
  /* >  with nb = 2: */
  /* > */
  /* >  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n): */
  /* > */
  /* >    (  1   1   u1  u1  u1 )           (  1   u1  u1  u1  u1  u1 ) */
  /* >    (  v1  1   1   u2  u2 )           (  1   1   u2  u2  u2  u2 ) */
  /* >    (  v1  v2  a   a   a  )           (  v1  1   a   a   a   a  ) */
  /* >    (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  ) */
  /* >    (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  ) */
  /* >    (  v1  v2  a   a   a  ) */
  /* > */
  /* >  where a denotes an element of the original matrix which is unchanged, */
  /* >  vi denotes an element of the vector defining H(i), and ui an element */
  /* >  of the vector defining G(i). */
  /* > \endverbatim */
  /* > */
  /*  ===================================================================== */
  /* Subroutine */ int dlabrd_(integer *m, integer *n, integer *nb, doublereal *
  	a, integer *lda, doublereal *d__, doublereal *e, doublereal *tauq, 
  	doublereal *taup, doublereal *x, integer *ldx, doublereal *y, integer 
  	*ldy)
  {
      /* System generated locals */
      integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2, 
  	    i__3;
  
      /* Local variables */
      integer i__;
      extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
  	    integer *), dgemv_(char *, integer *, integer *, doublereal *, 
  	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
  	    doublereal *, integer *), dlarfg_(integer *, doublereal *,
  	     doublereal *, integer *, doublereal *);
  
  
  /*  -- LAPACK auxiliary routine (version 3.7.1) -- */
  /*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
  /*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  /*     June 2017 */
  
  
  /*  ===================================================================== */
  
  
  /*     Quick return if possible */
  
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1 * 1;
      a -= a_offset;
      --d__;
      --e;
      --tauq;
      --taup;
      x_dim1 = *ldx;
      x_offset = 1 + x_dim1 * 1;
      x -= x_offset;
      y_dim1 = *ldy;
      y_offset = 1 + y_dim1 * 1;
      y -= y_offset;
  
      /* Function Body */
      if (*m <= 0 || *n <= 0) {
  	return 0;
      }
  
      if (*m >= *n) {
  
  /*        Reduce to upper bidiagonal form */
  
  	i__1 = *nb;
  	for (i__ = 1; i__ <= i__1; ++i__) {
  
  /*           Update A(i:m,i) */
  
  	    i__2 = *m - i__ + 1;
  	    i__3 = i__ - 1;
  	    dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda,
  		     &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + i__ * a_dim1], &
  		    c__1);
  	    i__2 = *m - i__ + 1;
  	    i__3 = i__ - 1;
  	    dgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx,
  		     &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + i__ * 
  		    a_dim1], &c__1);
  
  /*           Generate reflection Q(i) to annihilate A(i+1:m,i) */
  
  	    i__2 = *m - i__ + 1;
  /* Computing MIN */
  	    i__3 = i__ + 1;
  	    dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[f2cmin(i__3,*m) + i__ * 
  		    a_dim1], &c__1, &tauq[i__]);
  	    d__[i__] = a[i__ + i__ * a_dim1];
  	    if (i__ < *n) {
  		a[i__ + i__ * a_dim1] = 1.;
  
  /*              Compute Y(i+1:n,i) */
  
  		i__2 = *m - i__ + 1;
  		i__3 = *n - i__;
  		dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) * 
  			a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &
  			y[i__ + 1 + i__ * y_dim1], &c__1);
  		i__2 = *m - i__ + 1;
  		i__3 = i__ - 1;
  		dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], 
  			lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * 
  			y_dim1 + 1], &c__1);
  		i__2 = *n - i__;
  		i__3 = i__ - 1;
  		dgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + 
  			y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[
  			i__ + 1 + i__ * y_dim1], &c__1);
  		i__2 = *m - i__ + 1;
  		i__3 = i__ - 1;
  		dgemv_("Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1], 
  			ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * 
  			y_dim1 + 1], &c__1);
  		i__2 = i__ - 1;
  		i__3 = *n - i__;
  		dgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * 
  			a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, 
  			&y[i__ + 1 + i__ * y_dim1], &c__1);
  		i__2 = *n - i__;
  		dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
  
  /*              Update A(i,i+1:n) */
  
  		i__2 = *n - i__;
  		dgemv_("No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 + 
  			y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b5, &a[i__ + (
  			i__ + 1) * a_dim1], lda);
  		i__2 = i__ - 1;
  		i__3 = *n - i__;
  		dgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * 
  			a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b5, &a[
  			i__ + (i__ + 1) * a_dim1], lda);
  
  /*              Generate reflection P(i) to annihilate A(i,i+2:n) */
  
  		i__2 = *n - i__;
  /* Computing MIN */
  		i__3 = i__ + 2;
  		dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + f2cmin(
  			i__3,*n) * a_dim1], lda, &taup[i__]);
  		e[i__] = a[i__ + (i__ + 1) * a_dim1];
  		a[i__ + (i__ + 1) * a_dim1] = 1.;
  
  /*              Compute X(i+1:m,i) */
  
  		i__2 = *m - i__;
  		i__3 = *n - i__;
  		dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ 
  			+ 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1], 
  			lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1);
  		i__2 = *n - i__;
  		dgemv_("Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1], 
  			ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[
  			i__ * x_dim1 + 1], &c__1);
  		i__2 = *m - i__;
  		dgemv_("No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 + 
  			a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
  			i__ + 1 + i__ * x_dim1], &c__1);
  		i__2 = i__ - 1;
  		i__3 = *n - i__;
  		dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * 
  			a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, &
  			c_b16, &x[i__ * x_dim1 + 1], &c__1);
  		i__2 = *m - i__;
  		i__3 = i__ - 1;
  		dgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + 
  			x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
  			i__ + 1 + i__ * x_dim1], &c__1);
  		i__2 = *m - i__;
  		dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
  	    }
  /* L10: */
  	}
      } else {
  
  /*        Reduce to lower bidiagonal form */
  
  	i__1 = *nb;
  	for (i__ = 1; i__ <= i__1; ++i__) {
  
  /*           Update A(i,i:n) */
  
  	    i__2 = *n - i__ + 1;
  	    i__3 = i__ - 1;
  	    dgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy,
  		     &a[i__ + a_dim1], lda, &c_b5, &a[i__ + i__ * a_dim1], 
  		    lda);
  	    i__2 = i__ - 1;
  	    i__3 = *n - i__ + 1;
  	    dgemv_("Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1], 
  		    lda, &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + i__ * a_dim1],
  		     lda);
  
  /*           Generate reflection P(i) to annihilate A(i,i+1:n) */
  
  	    i__2 = *n - i__ + 1;
  /* Computing MIN */
  	    i__3 = i__ + 1;
  	    dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + f2cmin(i__3,*n) * 
  		    a_dim1], lda, &taup[i__]);
  	    d__[i__] = a[i__ + i__ * a_dim1];
  	    if (i__ < *m) {
  		a[i__ + i__ * a_dim1] = 1.;
  
  /*              Compute X(i+1:m,i) */
  
  		i__2 = *m - i__;
  		i__3 = *n - i__ + 1;
  		dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + i__ *
  			 a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &
  			x[i__ + 1 + i__ * x_dim1], &c__1);
  		i__2 = *n - i__ + 1;
  		i__3 = i__ - 1;
  		dgemv_("Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1], 
  			ldy, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * 
  			x_dim1 + 1], &c__1);
  		i__2 = *m - i__;
  		i__3 = i__ - 1;
  		dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + 
  			a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
  			i__ + 1 + i__ * x_dim1], &c__1);
  		i__2 = i__ - 1;
  		i__3 = *n - i__ + 1;
  		dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ * a_dim1 + 
  			1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ *
  			 x_dim1 + 1], &c__1);
  		i__2 = *m - i__;
  		i__3 = i__ - 1;
  		dgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + 
  			x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
  			i__ + 1 + i__ * x_dim1], &c__1);
  		i__2 = *m - i__;
  		dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
  
  /*              Update A(i+1:m,i) */
  
  		i__2 = *m - i__;
  		i__3 = i__ - 1;
  		dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + 
  			a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + 
  			1 + i__ * a_dim1], &c__1);
  		i__2 = *m - i__;
  		dgemv_("No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 + 
  			x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[
  			i__ + 1 + i__ * a_dim1], &c__1);
  
  /*              Generate reflection Q(i) to annihilate A(i+2:m,i) */
  
  		i__2 = *m - i__;
  /* Computing MIN */
  		i__3 = i__ + 2;
  		dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[f2cmin(i__3,*m) + 
  			i__ * a_dim1], &c__1, &tauq[i__]);
  		e[i__] = a[i__ + 1 + i__ * a_dim1];
  		a[i__ + 1 + i__ * a_dim1] = 1.;
  
  /*              Compute Y(i+1:n,i) */
  
  		i__2 = *m - i__;
  		i__3 = *n - i__;
  		dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + 
  			1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, 
  			&c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1);
  		i__2 = *m - i__;
  		i__3 = i__ - 1;
  		dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1],
  			 lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[
  			i__ * y_dim1 + 1], &c__1);
  		i__2 = *n - i__;
  		i__3 = i__ - 1;
  		dgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + 
  			y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[
  			i__ + 1 + i__ * y_dim1], &c__1);
  		i__2 = *m - i__;
  		dgemv_("Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1], 
  			ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[
  			i__ * y_dim1 + 1], &c__1);
  		i__2 = *n - i__;
  		dgemv_("Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1 
  			+ 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ 
  			+ 1 + i__ * y_dim1], &c__1);
  		i__2 = *n - i__;
  		dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
  	    }
  /* L20: */
  	}
      }
      return 0;
  
  /*     End of DLABRD */
  
  } /* dlabrd_ */
  
  