OpenBLAS/lapack-netlib/SRC/dlasd6.c

#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif

#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif

#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif

typedef blasint integer;

typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef int logical;
typedef short int shortlogical;
typedef char logical1;
typedef char integer1;

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

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

/* I/O stuff */

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

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

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

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

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

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

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

#define VOID void

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

typedef union Multitype Multitype;

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

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

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

#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}

/* procedure parameter types for -A and -C++ */

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

static float spow_ui(float x, integer n) {
	float pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
static double dpow_ui(double x, integer n) {
	double pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
#ifdef _MSC_VER
static _Fcomplex cpow_ui(complex x, integer n) {
	complex pow={1.0,0.0}; unsigned long int u;
		if(n != 0) {
		if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
		for(u = n; ; ) {
			if(u & 01) pow.r *= x.r, pow.i *= x.i;
			if(u >>= 1) x.r *= x.r, x.i *= x.i;
			else break;
		}
	}
	_Fcomplex p={pow.r, pow.i};
	return p;
}
#else
static _Complex float cpow_ui(_Complex float x, integer n) {
	_Complex float pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
#endif
#ifdef _MSC_VER
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
	_Dcomplex pow={1.0,0.0}; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
		for(u = n; ; ) {
			if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
			if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
			else break;
		}
	}
	_Dcomplex p = {pow._Val[0], pow._Val[1]};
	return p;
}
#else
static _Complex double zpow_ui(_Complex double x, integer n) {
	_Complex double pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
#endif
static integer pow_ii(integer x, integer n) {
	integer pow; unsigned long int u;
	if (n <= 0) {
		if (n == 0 || x == 1) pow = 1;
		else if (x != -1) pow = x == 0 ? 1/x : 0;
		else n = -n;
	}
	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
		u = n;
		for(pow = 1; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
	double m; integer i, mi;
	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
		if (w[i-1]>m) mi=i ,m=w[i-1];
	return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
	float m; integer i, mi;
	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
		if (w[i-1]>m) mi=i ,m=w[i-1];
	return mi-s+1;
}
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
	_Fcomplex zdotc = {0.0, 0.0};
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
			zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
			zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
		}
	}
	pCf(z) = zdotc;
}
#else
	_Complex float zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
		}
	}
	pCf(z) = zdotc;
}
#endif
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
	_Dcomplex zdotc = {0.0, 0.0};
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
			zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
			zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
		}
	}
	pCd(z) = zdotc;
}
#else
	_Complex double zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
		}
	}
	pCd(z) = zdotc;
}
#endif	
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
	_Fcomplex zdotc = {0.0, 0.0};
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
			zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
			zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
		}
	}
	pCf(z) = zdotc;
}
#else
	_Complex float zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cf(&x[i]) * Cf(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
		}
	}
	pCf(z) = zdotc;
}
#endif
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
	_Dcomplex zdotc = {0.0, 0.0};
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
			zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
			zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
		}
	}
	pCd(z) = zdotc;
}
#else
	_Complex double zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cd(&x[i]) * Cd(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
		}
	}
	pCd(z) = zdotc;
}
#endif
/*  -- translated by f2c (version 20000121).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/




/* Table of constant values */

static integer c__0 = 0;
static doublereal c_b7 = 1.;
static integer c__1 = 1;
static integer c_n1 = -1;

/* > \brief \b DLASD6 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 */
/* > Download DLASD6 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd6.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasd6.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasd6.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

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

/*       SUBROUTINE DLASD6( 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 */
/*       DOUBLE PRECISION   ALPHA, BETA, C, S */
/*       INTEGER            GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ), */
/*      $                   PERM( * ) */
/*       DOUBLE PRECISION   D( * ), DIFL( * ), DIFR( * ), */
/*      $                   GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ), */
/*      $                   VF( * ), VL( * ), WORK( * ), Z( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLASD6 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, DLASD1, handles the case in which all singular */
/* > values and singular vectors of the bidiagonal matrix are desired. */
/* > */
/* > DLASD6 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 DLASD6. 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 DLASD7. */
/* > */
/* >       The second stage consists of calculating the updated */
/* >       singular values. This is done by finding the roots of the */
/* >       secular equation via the routine DLASD4 (as called by DLASD8). */
/* >       This routine also updates VF and VL and computes the distances */
/* >       between the updated singular values and the old singular */
/* >       values. */
/* > */
/* > DLASD6 is called from DLASDA. */
/* > \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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION */
/* >         Contains the diagonal element associated with the added row. */
/* > \endverbatim */
/* > */
/* > \param[in,out] BETA */
/* > \verbatim */
/* >          BETA is DOUBLE PRECISION */
/* >         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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DLASD8 for details on DIFL and DIFR. */
/* > \endverbatim */
/* > */
/* > \param[out] Z */
/* > \verbatim */
/* >          Z is DOUBLE PRECISION 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 DOUBLE PRECISION */
/* >         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 DOUBLE PRECISION */
/* >         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 DOUBLE PRECISION 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 */ void dlasd6_(integer *icompq, integer *nl, integer *nr, 
	integer *sqre, doublereal *d__, doublereal *vf, doublereal *vl, 
	doublereal *alpha, doublereal *beta, integer *idxq, integer *perm, 
	integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum,
	 integer *ldgnum, doublereal *poles, doublereal *difl, doublereal *
	difr, doublereal *z__, integer *k, doublereal *c__, doublereal *s, 
	doublereal *work, integer *iwork, integer *info)
{
    /* System generated locals */
    integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, 
	    poles_dim1, poles_offset, i__1;
    doublereal d__1, d__2;

    /* Local variables */
    integer idxc, idxp, ivfw, ivlw, i__, m, n;
    extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    integer n1, n2;
    extern /* Subroutine */ void dlasd7_(integer *, integer *, integer *, 
	    integer *, integer *, doublereal *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, integer *, integer *, 
	    integer *, integer *, integer *, integer *, integer *, doublereal 
	    *, integer *, doublereal *, doublereal *, integer *), dlasd8_(
	    integer *, integer *, doublereal *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, integer *, doublereal *,
	     doublereal *, integer *);
    integer iw;
    extern /* Subroutine */ void dlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, integer *), dlamrg_(integer *, integer *, 
	    doublereal *, integer *, integer *, integer *);
    integer isigma;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    doublereal 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_("DLASD6", &i__1, (ftnlen)6);
	return;
    }

/*     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 DLASD7 and DLASD8. */

    isigma = 1;
    iw = isigma + n;
    ivfw = iw + m;
    ivlw = ivfw + m;

    idx = 1;
    idxc = idx + n;
    idxp = idxc + n;

/*     Scale. */

/* Computing MAX */
    d__1 = abs(*alpha), d__2 = abs(*beta);
    orgnrm = f2cmax(d__1,d__2);
    d__[*nl + 1] = 0.;
    i__1 = n;
    for (i__ = 1; i__ <= i__1; ++i__) {
	if ((d__1 = d__[i__], abs(d__1)) > orgnrm) {
	    orgnrm = (d__1 = d__[i__], abs(d__1));
	}
/* L10: */
    }
    dlascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info);
    *alpha /= orgnrm;
    *beta /= orgnrm;

/*     Sort and Deflate singular values. */

    dlasd7_(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. */

    dlasd8_(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;
    }

/*     Save the poles if ICOMPQ = 1. */

    if (*icompq == 1) {
	dcopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1);
	dcopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1);
    }

/*     Unscale. */

    dlascl_("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;
    dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]);

    return;

/*     End of DLASD6 */

} /* dlasd6_ */