OpenBLAS/lapack-netlib/SRC/slasd3.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__1 = 1;
static integer c__0 = 0;
static real c_b13 = 1.f;
static real c_b26 = 0.f;

/* > \brief \b SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in
 D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc. */

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

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

/* > \htmlonly */
/* > Download SLASD3 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasd3.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasd3.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasd3.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

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

/*       SUBROUTINE SLASD3( NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2, */
/*                          LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z, */
/*                          INFO ) */

/*       INTEGER            INFO, K, LDQ, LDU, LDU2, LDVT, LDVT2, NL, NR, */
/*      $                   SQRE */
/*       INTEGER            CTOT( * ), IDXC( * ) */
/*       REAL               D( * ), DSIGMA( * ), Q( LDQ, * ), U( LDU, * ), */
/*      $                   U2( LDU2, * ), VT( LDVT, * ), VT2( LDVT2, * ), */
/*      $                   Z( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SLASD3 finds all the square roots of the roots of the secular */
/* > equation, as defined by the values in D and Z.  It makes the */
/* > appropriate calls to SLASD4 and then updates the singular */
/* > vectors by matrix multiplication. */
/* > */
/* > This code makes very mild assumptions about floating point */
/* > arithmetic. It will work on machines with a guard digit in */
/* > add/subtract, or on those binary machines without guard digits */
/* > which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2. */
/* > It could conceivably fail on hexadecimal or decimal machines */
/* > without guard digits, but we know of none. */
/* > */
/* > SLASD3 is called from SLASD1. */
/* > \endverbatim */

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

/* > \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 N = NL + NR + 1 rows and */
/* >         M = N + SQRE >= N columns. */
/* > \endverbatim */
/* > */
/* > \param[in] K */
/* > \verbatim */
/* >          K is INTEGER */
/* >         The size of the secular equation, 1 =< K = < N. */
/* > \endverbatim */
/* > */
/* > \param[out] D */
/* > \verbatim */
/* >          D is REAL array, dimension(K) */
/* >         On exit the square roots of the roots of the secular equation, */
/* >         in ascending order. */
/* > \endverbatim */
/* > */
/* > \param[out] Q */
/* > \verbatim */
/* >          Q is REAL array, dimension (LDQ,K) */
/* > \endverbatim */
/* > */
/* > \param[in] LDQ */
/* > \verbatim */
/* >          LDQ is INTEGER */
/* >         The leading dimension of the array Q.  LDQ >= K. */
/* > \endverbatim */
/* > */
/* > \param[in,out] DSIGMA */
/* > \verbatim */
/* >          DSIGMA is REAL array, dimension(K) */
/* >         The first K elements of this array contain the old roots */
/* >         of the deflated updating problem.  These are the poles */
/* >         of the secular equation. */
/* > \endverbatim */
/* > */
/* > \param[out] U */
/* > \verbatim */
/* >          U is REAL array, dimension (LDU, N) */
/* >         The last N - K columns of this matrix contain the deflated */
/* >         left singular vectors. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* >          LDU is INTEGER */
/* >         The leading dimension of the array U.  LDU >= N. */
/* > \endverbatim */
/* > */
/* > \param[in] U2 */
/* > \verbatim */
/* >          U2 is REAL array, dimension (LDU2, N) */
/* >         The first K columns of this matrix contain the non-deflated */
/* >         left singular vectors for the split problem. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU2 */
/* > \verbatim */
/* >          LDU2 is INTEGER */
/* >         The leading dimension of the array U2.  LDU2 >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] VT */
/* > \verbatim */
/* >          VT is REAL array, dimension (LDVT, M) */
/* >         The last M - K columns of VT**T contain the deflated */
/* >         right singular vectors. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVT */
/* > \verbatim */
/* >          LDVT is INTEGER */
/* >         The leading dimension of the array VT.  LDVT >= N. */
/* > \endverbatim */
/* > */
/* > \param[in,out] VT2 */
/* > \verbatim */
/* >          VT2 is REAL array, dimension (LDVT2, N) */
/* >         The first K columns of VT2**T contain the non-deflated */
/* >         right singular vectors for the split problem. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVT2 */
/* > \verbatim */
/* >          LDVT2 is INTEGER */
/* >         The leading dimension of the array VT2.  LDVT2 >= N. */
/* > \endverbatim */
/* > */
/* > \param[in] IDXC */
/* > \verbatim */
/* >          IDXC is INTEGER array, dimension (N) */
/* >         The permutation used to arrange the columns of U (and rows of */
/* >         VT) into three groups:  the first group contains non-zero */
/* >         entries only at and above (or before) NL +1; the second */
/* >         contains non-zero entries only at and below (or after) NL+2; */
/* >         and the third is dense. The first column of U and the row of */
/* >         VT are treated separately, however. */
/* > */
/* >         The rows of the singular vectors found by SLASD4 */
/* >         must be likewise permuted before the matrix multiplies can */
/* >         take place. */
/* > \endverbatim */
/* > */
/* > \param[in] CTOT */
/* > \verbatim */
/* >          CTOT is INTEGER array, dimension (4) */
/* >         A count of the total number of the various types of columns */
/* >         in U (or rows in VT), as described in IDXC. The fourth column */
/* >         type is any column which has been deflated. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Z */
/* > \verbatim */
/* >          Z is REAL array, dimension (K) */
/* >         The first K elements of this array contain the components */
/* >         of the deflation-adjusted updating row vector. */
/* > \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 2017 */

/* > \ingroup OTHERauxiliary */

/* > \par Contributors: */
/*  ================== */
/* > */
/* >     Ming Gu and Huan Ren, Computer Science Division, University of */
/* >     California at Berkeley, USA */
/* > */
/*  ===================================================================== */
/* Subroutine */ void slasd3_(integer *nl, integer *nr, integer *sqre, integer 
	*k, real *d__, real *q, integer *ldq, real *dsigma, real *u, integer *
	ldu, real *u2, integer *ldu2, real *vt, integer *ldvt, real *vt2, 
	integer *ldvt2, integer *idxc, integer *ctot, real *z__, integer *
	info)
{
    /* System generated locals */
    integer q_dim1, q_offset, u_dim1, u_offset, u2_dim1, u2_offset, vt_dim1, 
	    vt_offset, vt2_dim1, vt2_offset, i__1, i__2;
    real r__1, r__2;

    /* Local variables */
    real temp;
    extern real snrm2_(integer *, real *, integer *);
    integer i__, j, m, n, ctemp;
    extern /* Subroutine */ void sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    integer ktemp;
    extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *, 
	    integer *);
    extern real slamc3_(real *, real *);
    extern /* Subroutine */ void slasd4_(integer *, integer *, real *, real *, 
	    real *, real *, real *, real *, integer *);
    integer jc;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern void slascl_(
	    char *, integer *, integer *, real *, real *, integer *, integer *
	    , real *, integer *, integer *), slacpy_(char *, integer *
	    , integer *, real *, integer *, real *, integer *);
    real rho;
    integer nlp1, nlp2, nrp1;


/*  -- 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 */


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


/*     Test the input parameters. */

    /* Parameter adjustments */
    --d__;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    --dsigma;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1 * 1;
    u -= u_offset;
    u2_dim1 = *ldu2;
    u2_offset = 1 + u2_dim1 * 1;
    u2 -= u2_offset;
    vt_dim1 = *ldvt;
    vt_offset = 1 + vt_dim1 * 1;
    vt -= vt_offset;
    vt2_dim1 = *ldvt2;
    vt2_offset = 1 + vt2_dim1 * 1;
    vt2 -= vt2_offset;
    --idxc;
    --ctot;
    --z__;

    /* Function Body */
    *info = 0;

    if (*nl < 1) {
	*info = -1;
    } else if (*nr < 1) {
	*info = -2;
    } else if (*sqre != 1 && *sqre != 0) {
	*info = -3;
    }

    n = *nl + *nr + 1;
    m = n + *sqre;
    nlp1 = *nl + 1;
    nlp2 = *nl + 2;

    if (*k < 1 || *k > n) {
	*info = -4;
    } else if (*ldq < *k) {
	*info = -7;
    } else if (*ldu < n) {
	*info = -10;
    } else if (*ldu2 < n) {
	*info = -12;
    } else if (*ldvt < m) {
	*info = -14;
    } else if (*ldvt2 < m) {
	*info = -16;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SLASD3", &i__1, (ftnlen)6);
	return;
    }

/*     Quick return if possible */

    if (*k == 1) {
	d__[1] = abs(z__[1]);
	scopy_(&m, &vt2[vt2_dim1 + 1], ldvt2, &vt[vt_dim1 + 1], ldvt);
	if (z__[1] > 0.f) {
	    scopy_(&n, &u2[u2_dim1 + 1], &c__1, &u[u_dim1 + 1], &c__1);
	} else {
	    i__1 = n;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		u[i__ + u_dim1] = -u2[i__ + u2_dim1];
/* L10: */
	    }
	}
	return;
    }

/*     Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can */
/*     be computed with high relative accuracy (barring over/underflow). */
/*     This is a problem on machines without a guard digit in */
/*     add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */
/*     The following code replaces DSIGMA(I) by 2*DSIGMA(I)-DSIGMA(I), */
/*     which on any of these machines zeros out the bottommost */
/*     bit of DSIGMA(I) if it is 1; this makes the subsequent */
/*     subtractions DSIGMA(I)-DSIGMA(J) unproblematic when cancellation */
/*     occurs. On binary machines with a guard digit (almost all */
/*     machines) it does not change DSIGMA(I) at all. On hexadecimal */
/*     and decimal machines with a guard digit, it slightly */
/*     changes the bottommost bits of DSIGMA(I). It does not account */
/*     for hexadecimal or decimal machines without guard digits */
/*     (we know of none). We use a subroutine call to compute */
/*     2*DSIGMA(I) to prevent optimizing compilers from eliminating */
/*     this code. */

    i__1 = *k;
    for (i__ = 1; i__ <= i__1; ++i__) {
	dsigma[i__] = slamc3_(&dsigma[i__], &dsigma[i__]) - dsigma[i__];
/* L20: */
    }

/*     Keep a copy of Z. */

    scopy_(k, &z__[1], &c__1, &q[q_offset], &c__1);

/*     Normalize Z. */

    rho = snrm2_(k, &z__[1], &c__1);
    slascl_("G", &c__0, &c__0, &rho, &c_b13, k, &c__1, &z__[1], k, info);
    rho *= rho;

/*     Find the new singular values. */

    i__1 = *k;
    for (j = 1; j <= i__1; ++j) {
	slasd4_(k, &j, &dsigma[1], &z__[1], &u[j * u_dim1 + 1], &rho, &d__[j],
		 &vt[j * vt_dim1 + 1], info);

/*        If the zero finder fails, report the convergence failure. */

	if (*info != 0) {
	    return;
	}
/* L30: */
    }

/*     Compute updated Z. */

    i__1 = *k;
    for (i__ = 1; i__ <= i__1; ++i__) {
	z__[i__] = u[i__ + *k * u_dim1] * vt[i__ + *k * vt_dim1];
	i__2 = i__ - 1;
	for (j = 1; j <= i__2; ++j) {
	    z__[i__] *= u[i__ + j * u_dim1] * vt[i__ + j * vt_dim1] / (dsigma[
		    i__] - dsigma[j]) / (dsigma[i__] + dsigma[j]);
/* L40: */
	}
	i__2 = *k - 1;
	for (j = i__; j <= i__2; ++j) {
	    z__[i__] *= u[i__ + j * u_dim1] * vt[i__ + j * vt_dim1] / (dsigma[
		    i__] - dsigma[j + 1]) / (dsigma[i__] + dsigma[j + 1]);
/* L50: */
	}
	r__2 = sqrt((r__1 = z__[i__], abs(r__1)));
	z__[i__] = r_sign(&r__2, &q[i__ + q_dim1]);
/* L60: */
    }

/*     Compute left singular vectors of the modified diagonal matrix, */
/*     and store related information for the right singular vectors. */

    i__1 = *k;
    for (i__ = 1; i__ <= i__1; ++i__) {
	vt[i__ * vt_dim1 + 1] = z__[1] / u[i__ * u_dim1 + 1] / vt[i__ * 
		vt_dim1 + 1];
	u[i__ * u_dim1 + 1] = -1.f;
	i__2 = *k;
	for (j = 2; j <= i__2; ++j) {
	    vt[j + i__ * vt_dim1] = z__[j] / u[j + i__ * u_dim1] / vt[j + i__ 
		    * vt_dim1];
	    u[j + i__ * u_dim1] = dsigma[j] * vt[j + i__ * vt_dim1];
/* L70: */
	}
	temp = snrm2_(k, &u[i__ * u_dim1 + 1], &c__1);
	q[i__ * q_dim1 + 1] = u[i__ * u_dim1 + 1] / temp;
	i__2 = *k;
	for (j = 2; j <= i__2; ++j) {
	    jc = idxc[j];
	    q[j + i__ * q_dim1] = u[jc + i__ * u_dim1] / temp;
/* L80: */
	}
/* L90: */
    }

/*     Update the left singular vector matrix. */

    if (*k == 2) {
	sgemm_("N", "N", &n, k, k, &c_b13, &u2[u2_offset], ldu2, &q[q_offset],
		 ldq, &c_b26, &u[u_offset], ldu);
	goto L100;
    }
    if (ctot[1] > 0) {
	sgemm_("N", "N", nl, k, &ctot[1], &c_b13, &u2[(u2_dim1 << 1) + 1], 
		ldu2, &q[q_dim1 + 2], ldq, &c_b26, &u[u_dim1 + 1], ldu);
	if (ctot[3] > 0) {
	    ktemp = ctot[1] + 2 + ctot[2];
	    sgemm_("N", "N", nl, k, &ctot[3], &c_b13, &u2[ktemp * u2_dim1 + 1]
		    , ldu2, &q[ktemp + q_dim1], ldq, &c_b13, &u[u_dim1 + 1], 
		    ldu);
	}
    } else if (ctot[3] > 0) {
	ktemp = ctot[1] + 2 + ctot[2];
	sgemm_("N", "N", nl, k, &ctot[3], &c_b13, &u2[ktemp * u2_dim1 + 1], 
		ldu2, &q[ktemp + q_dim1], ldq, &c_b26, &u[u_dim1 + 1], ldu);
    } else {
	slacpy_("F", nl, k, &u2[u2_offset], ldu2, &u[u_offset], ldu);
    }
    scopy_(k, &q[q_dim1 + 1], ldq, &u[nlp1 + u_dim1], ldu);
    ktemp = ctot[1] + 2;
    ctemp = ctot[2] + ctot[3];
    sgemm_("N", "N", nr, k, &ctemp, &c_b13, &u2[nlp2 + ktemp * u2_dim1], ldu2,
	     &q[ktemp + q_dim1], ldq, &c_b26, &u[nlp2 + u_dim1], ldu);

/*     Generate the right singular vectors. */

L100:
    i__1 = *k;
    for (i__ = 1; i__ <= i__1; ++i__) {
	temp = snrm2_(k, &vt[i__ * vt_dim1 + 1], &c__1);
	q[i__ + q_dim1] = vt[i__ * vt_dim1 + 1] / temp;
	i__2 = *k;
	for (j = 2; j <= i__2; ++j) {
	    jc = idxc[j];
	    q[i__ + j * q_dim1] = vt[jc + i__ * vt_dim1] / temp;
/* L110: */
	}
/* L120: */
    }

/*     Update the right singular vector matrix. */

    if (*k == 2) {
	sgemm_("N", "N", k, &m, k, &c_b13, &q[q_offset], ldq, &vt2[vt2_offset]
		, ldvt2, &c_b26, &vt[vt_offset], ldvt);
	return;
    }
    ktemp = ctot[1] + 1;
    sgemm_("N", "N", k, &nlp1, &ktemp, &c_b13, &q[q_dim1 + 1], ldq, &vt2[
	    vt2_dim1 + 1], ldvt2, &c_b26, &vt[vt_dim1 + 1], ldvt);
    ktemp = ctot[1] + 2 + ctot[2];
    if (ktemp <= *ldvt2) {
	sgemm_("N", "N", k, &nlp1, &ctot[3], &c_b13, &q[ktemp * q_dim1 + 1], 
		ldq, &vt2[ktemp + vt2_dim1], ldvt2, &c_b13, &vt[vt_dim1 + 1], 
		ldvt);
    }

    ktemp = ctot[1] + 1;
    nrp1 = *nr + *sqre;
    if (ktemp > 1) {
	i__1 = *k;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    q[i__ + ktemp * q_dim1] = q[i__ + q_dim1];
/* L130: */
	}
	i__1 = m;
	for (i__ = nlp2; i__ <= i__1; ++i__) {
	    vt2[ktemp + i__ * vt2_dim1] = vt2[i__ * vt2_dim1 + 1];
/* L140: */
	}
    }
    ctemp = ctot[2] + 1 + ctot[3];
    sgemm_("N", "N", k, &nrp1, &ctemp, &c_b13, &q[ktemp * q_dim1 + 1], ldq, &
	    vt2[ktemp + nlp2 * vt2_dim1], ldvt2, &c_b26, &vt[nlp2 * vt_dim1 + 
	    1], ldvt);

    return;

/*     End of SLASD3 */

} /* slasd3_ */