OpenBLAS/lapack-netlib/SRC/sbdsqr.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 blasint logical;

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++ */


#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_b15 = -.125;
static integer c__1 = 1;
static real c_b49 = 1.f;
static real c_b72 = -1.f;

/* > \brief \b SBDSQR */

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

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

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

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

/*       SUBROUTINE SBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, */
/*                          LDU, C, LDC, WORK, INFO ) */

/*       CHARACTER          UPLO */
/*       INTEGER            INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU */
/*       REAL               C( LDC, * ), D( * ), E( * ), U( LDU, * ), */
/*      $                   VT( LDVT, * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SBDSQR computes the singular values and, optionally, the right and/or */
/* > left singular vectors from the singular value decomposition (SVD) of */
/* > a real N-by-N (upper or lower) bidiagonal matrix B using the implicit */
/* > zero-shift QR algorithm.  The SVD of B has the form */
/* > */
/* >    B = Q * S * P**T */
/* > */
/* > where S is the diagonal matrix of singular values, Q is an orthogonal */
/* > matrix of left singular vectors, and P is an orthogonal matrix of */
/* > right singular vectors.  If left singular vectors are requested, this */
/* > subroutine actually returns U*Q instead of Q, and, if right singular */
/* > vectors are requested, this subroutine returns P**T*VT instead of */
/* > P**T, for given real input matrices U and VT.  When U and VT are the */
/* > orthogonal matrices that reduce a general matrix A to bidiagonal */
/* > form:  A = U*B*VT, as computed by SGEBRD, then */
/* > */
/* >    A = (U*Q) * S * (P**T*VT) */
/* > */
/* > is the SVD of A.  Optionally, the subroutine may also compute Q**T*C */
/* > for a given real input matrix C. */
/* > */
/* > See "Computing  Small Singular Values of Bidiagonal Matrices With */
/* > Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, */
/* > LAPACK Working Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11, */
/* > no. 5, pp. 873-912, Sept 1990) and */
/* > "Accurate singular values and differential qd algorithms," by */
/* > B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics */
/* > Department, University of California at Berkeley, July 1992 */
/* > for a detailed description of the algorithm. */
/* > \endverbatim */

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

/* > \param[in] UPLO */
/* > \verbatim */
/* >          UPLO is CHARACTER*1 */
/* >          = 'U':  B is upper bidiagonal; */
/* >          = 'L':  B is lower bidiagonal. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix B.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NCVT */
/* > \verbatim */
/* >          NCVT is INTEGER */
/* >          The number of columns of the matrix VT. NCVT >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NRU */
/* > \verbatim */
/* >          NRU is INTEGER */
/* >          The number of rows of the matrix U. NRU >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NCC */
/* > \verbatim */
/* >          NCC is INTEGER */
/* >          The number of columns of the matrix C. NCC >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* >          D is REAL array, dimension (N) */
/* >          On entry, the n diagonal elements of the bidiagonal matrix B. */
/* >          On exit, if INFO=0, the singular values of B in decreasing */
/* >          order. */
/* > \endverbatim */
/* > */
/* > \param[in,out] E */
/* > \verbatim */
/* >          E is REAL array, dimension (N-1) */
/* >          On entry, the N-1 offdiagonal elements of the bidiagonal */
/* >          matrix B. */
/* >          On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E */
/* >          will contain the diagonal and superdiagonal elements of a */
/* >          bidiagonal matrix orthogonally equivalent to the one given */
/* >          as input. */
/* > \endverbatim */
/* > */
/* > \param[in,out] VT */
/* > \verbatim */
/* >          VT is REAL array, dimension (LDVT, NCVT) */
/* >          On entry, an N-by-NCVT matrix VT. */
/* >          On exit, VT is overwritten by P**T * VT. */
/* >          Not referenced if NCVT = 0. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVT */
/* > \verbatim */
/* >          LDVT is INTEGER */
/* >          The leading dimension of the array VT. */
/* >          LDVT >= f2cmax(1,N) if NCVT > 0; LDVT >= 1 if NCVT = 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] U */
/* > \verbatim */
/* >          U is REAL array, dimension (LDU, N) */
/* >          On entry, an NRU-by-N matrix U. */
/* >          On exit, U is overwritten by U * Q. */
/* >          Not referenced if NRU = 0. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* >          LDU is INTEGER */
/* >          The leading dimension of the array U.  LDU >= f2cmax(1,NRU). */
/* > \endverbatim */
/* > */
/* > \param[in,out] C */
/* > \verbatim */
/* >          C is REAL array, dimension (LDC, NCC) */
/* >          On entry, an N-by-NCC matrix C. */
/* >          On exit, C is overwritten by Q**T * C. */
/* >          Not referenced if NCC = 0. */
/* > \endverbatim */
/* > */
/* > \param[in] LDC */
/* > \verbatim */
/* >          LDC is INTEGER */
/* >          The leading dimension of the array C. */
/* >          LDC >= f2cmax(1,N) if NCC > 0; LDC >=1 if NCC = 0. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL array, dimension (4*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 NCVT = NRU = NCC = 0, */
/* >                = 1, a split was marked by a positive value in E */
/* >                = 2, current block of Z not diagonalized after 30*N */
/* >                     iterations (in inner while loop) */
/* >                = 3, termination criterion of outer while loop not met */
/* >                     (program created more than N unreduced blocks) */
/* >             else NCVT = NRU = NCC = 0, */
/* >                   the algorithm did not converge; D and E contain the */
/* >                   elements of a bidiagonal matrix which is orthogonally */
/* >                   similar to the input matrix B;  if INFO = i, i */
/* >                   elements of E have not converged to zero. */
/* > \endverbatim */

/* > \par Internal Parameters: */
/*  ========================= */
/* > */
/* > \verbatim */
/* >  TOLMUL  REAL, default = f2cmax(10,f2cmin(100,EPS**(-1/8))) */
/* >          TOLMUL controls the convergence criterion of the QR loop. */
/* >          If it is positive, TOLMUL*EPS is the desired relative */
/* >             precision in the computed singular values. */
/* >          If it is negative, abs(TOLMUL*EPS*sigma_max) is the */
/* >             desired absolute accuracy in the computed singular */
/* >             values (corresponds to relative accuracy */
/* >             abs(TOLMUL*EPS) in the largest singular value. */
/* >          abs(TOLMUL) should be between 1 and 1/EPS, and preferably */
/* >             between 10 (for fast convergence) and .1/EPS */
/* >             (for there to be some accuracy in the results). */
/* >          Default is to lose at either one eighth or 2 of the */
/* >             available decimal digits in each computed singular value */
/* >             (whichever is smaller). */
/* > */
/* >  MAXITR  INTEGER, default = 6 */
/* >          MAXITR controls the maximum number of passes of the */
/* >          algorithm through its inner loop. The algorithms stops */
/* >          (and so fails to converge) if the number of passes */
/* >          through the inner loop exceeds MAXITR*N**2. */
/* > \endverbatim */

/* > \par Note: */
/*  =========== */
/* > */
/* > \verbatim */
/* >  Bug report from Cezary Dendek. */
/* >  On March 23rd 2017, the INTEGER variable MAXIT = MAXITR*N**2 is */
/* >  removed since it can overflow pretty easily (for N larger or equal */
/* >  than 18,919). We instead use MAXITDIVN = MAXITR*N. */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \date June 2017 */

/* > \ingroup auxOTHERcomputational */

/*  ===================================================================== */
/* Subroutine */ void sbdsqr_(char *uplo, integer *n, integer *ncvt, integer *
	nru, integer *ncc, real *d__, real *e, real *vt, integer *ldvt, real *
	u, integer *ldu, real *c__, integer *ldc, real *work, integer *info)
{
    /* System generated locals */
    integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, 
	    i__2;
    real r__1, r__2, r__3, r__4;
    doublereal d__1;

    /* Local variables */
    real abse;
    integer idir;
    real abss;
    integer oldm;
    real cosl;
    integer isub, iter;
    real unfl, sinl, cosr, smin, smax, sinr;
    extern /* Subroutine */ void srot_(integer *, real *, integer *, real *, 
	    integer *, real *, real *);
    integer iterdivn;
    extern /* Subroutine */ void slas2_(real *, real *, real *, real *, real *)
	    ;
    real f, g, h__;
    integer i__, j, m;
    real r__;
    extern logical lsame_(char *, char *);
    real oldcs;
    extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
    integer oldll;
    real shift, sigmn, oldsn, sminl;
    extern /* Subroutine */ void slasr_(char *, char *, char *, integer *, 
	    integer *, real *, real *, real *, integer *);
    real sigmx;
    logical lower;
    extern /* Subroutine */ void sswap_(integer *, real *, integer *, real *, 
	    integer *);
    integer maxitdivn;
    extern /* Subroutine */ void slasq1_(integer *, real *, real *, real *, 
	    integer *), slasv2_(real *, real *, real *, real *, real *, real *
	    , real *, real *, real *);
    real cs;
    integer ll;
    real sn, mu;
    extern real slamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    real sminoa;
    extern /* Subroutine */ void slartg_(real *, real *, real *, real *, real *
	    );
    real thresh;
    logical rotate;
    integer nm1;
    real tolmul;
    integer nm12, nm13, lll;
    real eps, sll, tol;


/*  -- LAPACK computational 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__;
    --e;
    vt_dim1 = *ldvt;
    vt_offset = 1 + vt_dim1 * 1;
    vt -= vt_offset;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1 * 1;
    u -= u_offset;
    c_dim1 = *ldc;
    c_offset = 1 + c_dim1 * 1;
    c__ -= c_offset;
    --work;

    /* Function Body */
    *info = 0;
    lower = lsame_(uplo, "L");
    if (! lsame_(uplo, "U") && ! lower) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*ncvt < 0) {
	*info = -3;
    } else if (*nru < 0) {
	*info = -4;
    } else if (*ncc < 0) {
	*info = -5;
    } else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < f2cmax(1,*n)) {
	*info = -9;
    } else if (*ldu < f2cmax(1,*nru)) {
	*info = -11;
    } else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < f2cmax(1,*n)) {
	*info = -13;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SBDSQR", &i__1, (ftnlen)6);
	return;
    }
    if (*n == 0) {
	return;
    }
    if (*n == 1) {
	goto L160;
    }

/*     ROTATE is true if any singular vectors desired, false otherwise */

    rotate = *ncvt > 0 || *nru > 0 || *ncc > 0;

/*     If no singular vectors desired, use qd algorithm */

    if (! rotate) {
	slasq1_(n, &d__[1], &e[1], &work[1], info);

/*     If INFO equals 2, dqds didn't finish, try to finish */

	if (*info != 2) {
	    return;
	}
	*info = 0;
    }

    nm1 = *n - 1;
    nm12 = nm1 + nm1;
    nm13 = nm12 + nm1;
    idir = 0;

/*     Get machine constants */

    eps = slamch_("Epsilon");
    unfl = slamch_("Safe minimum");

/*     If matrix lower bidiagonal, rotate to be upper bidiagonal */
/*     by applying Givens rotations on the left */

    if (lower) {
	i__1 = *n - 1;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    slartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
	    d__[i__] = r__;
	    e[i__] = sn * d__[i__ + 1];
	    d__[i__ + 1] = cs * d__[i__ + 1];
	    work[i__] = cs;
	    work[nm1 + i__] = sn;
/* L10: */
	}

/*        Update singular vectors if desired */

	if (*nru > 0) {
	    slasr_("R", "V", "F", nru, n, &work[1], &work[*n], &u[u_offset], 
		    ldu);
	}
	if (*ncc > 0) {
	    slasr_("L", "V", "F", n, ncc, &work[1], &work[*n], &c__[c_offset],
		     ldc);
	}
    }

/*     Compute singular values to relative accuracy TOL */
/*     (By setting TOL to be negative, algorithm will compute */
/*     singular values to absolute accuracy ABS(TOL)*norm(input matrix)) */

/* Computing MAX */
/* Computing MIN */
    d__1 = (doublereal) eps;
    r__3 = 100.f, r__4 = pow_dd(&d__1, &c_b15);
    r__1 = 10.f, r__2 = f2cmin(r__3,r__4);
    tolmul = f2cmax(r__1,r__2);
    tol = tolmul * eps;

/*     Compute approximate maximum, minimum singular values */

    smax = 0.f;
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
	r__2 = smax, r__3 = (r__1 = d__[i__], abs(r__1));
	smax = f2cmax(r__2,r__3);
/* L20: */
    }
    i__1 = *n - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
	r__2 = smax, r__3 = (r__1 = e[i__], abs(r__1));
	smax = f2cmax(r__2,r__3);
/* L30: */
    }
    sminl = 0.f;
    if (tol >= 0.f) {

/*        Relative accuracy desired */

	sminoa = abs(d__[1]);
	if (sminoa == 0.f) {
	    goto L50;
	}
	mu = sminoa;
	i__1 = *n;
	for (i__ = 2; i__ <= i__1; ++i__) {
	    mu = (r__2 = d__[i__], abs(r__2)) * (mu / (mu + (r__1 = e[i__ - 1]
		    , abs(r__1))));
	    sminoa = f2cmin(sminoa,mu);
	    if (sminoa == 0.f) {
		goto L50;
	    }
/* L40: */
	}
L50:
	sminoa /= sqrt((real) (*n));
/* Computing MAX */
	r__1 = tol * sminoa, r__2 = *n * (*n * unfl) * 6;
	thresh = f2cmax(r__1,r__2);
    } else {

/*        Absolute accuracy desired */

/* Computing MAX */
	r__1 = abs(tol) * smax, r__2 = *n * (*n * unfl) * 6;
	thresh = f2cmax(r__1,r__2);
    }

/*     Prepare for main iteration loop for the singular values */
/*     (MAXIT is the maximum number of passes through the inner */
/*     loop permitted before nonconvergence signalled.) */

    maxitdivn = *n * 6;
    iterdivn = 0;
    iter = -1;
    oldll = -1;
    oldm = -1;

/*     M points to last element of unconverged part of matrix */

    m = *n;

/*     Begin main iteration loop */

L60:

/*     Check for convergence or exceeding iteration count */

    if (m <= 1) {
	goto L160;
    }

    if (iter >= *n) {
	iter -= *n;
	++iterdivn;
	if (iterdivn >= maxitdivn) {
	    goto L200;
	}
    }

/*     Find diagonal block of matrix to work on */

    if (tol < 0.f && (r__1 = d__[m], abs(r__1)) <= thresh) {
	d__[m] = 0.f;
    }
    smax = (r__1 = d__[m], abs(r__1));
    smin = smax;
    i__1 = m - 1;
    for (lll = 1; lll <= i__1; ++lll) {
	ll = m - lll;
	abss = (r__1 = d__[ll], abs(r__1));
	abse = (r__1 = e[ll], abs(r__1));
	if (tol < 0.f && abss <= thresh) {
	    d__[ll] = 0.f;
	}
	if (abse <= thresh) {
	    goto L80;
	}
	smin = f2cmin(smin,abss);
/* Computing MAX */
	r__1 = f2cmax(smax,abss);
	smax = f2cmax(r__1,abse);
/* L70: */
    }
    ll = 0;
    goto L90;
L80:
    e[ll] = 0.f;

/*     Matrix splits since E(LL) = 0 */

    if (ll == m - 1) {

/*        Convergence of bottom singular value, return to top of loop */

	--m;
	goto L60;
    }
L90:
    ++ll;

/*     E(LL) through E(M-1) are nonzero, E(LL-1) is zero */

    if (ll == m - 1) {

/*        2 by 2 block, handle separately */

	slasv2_(&d__[m - 1], &e[m - 1], &d__[m], &sigmn, &sigmx, &sinr, &cosr,
		 &sinl, &cosl);
	d__[m - 1] = sigmx;
	e[m - 1] = 0.f;
	d__[m] = sigmn;

/*        Compute singular vectors, if desired */

	if (*ncvt > 0) {
	    srot_(ncvt, &vt[m - 1 + vt_dim1], ldvt, &vt[m + vt_dim1], ldvt, &
		    cosr, &sinr);
	}
	if (*nru > 0) {
	    srot_(nru, &u[(m - 1) * u_dim1 + 1], &c__1, &u[m * u_dim1 + 1], &
		    c__1, &cosl, &sinl);
	}
	if (*ncc > 0) {
	    srot_(ncc, &c__[m - 1 + c_dim1], ldc, &c__[m + c_dim1], ldc, &
		    cosl, &sinl);
	}
	m += -2;
	goto L60;
    }

/*     If working on new submatrix, choose shift direction */
/*     (from larger end diagonal element towards smaller) */

    if (ll > oldm || m < oldll) {
	if ((r__1 = d__[ll], abs(r__1)) >= (r__2 = d__[m], abs(r__2))) {

/*           Chase bulge from top (big end) to bottom (small end) */

	    idir = 1;
	} else {

/*           Chase bulge from bottom (big end) to top (small end) */

	    idir = 2;
	}
    }

/*     Apply convergence tests */

    if (idir == 1) {

/*        Run convergence test in forward direction */
/*        First apply standard test to bottom of matrix */

	if ((r__2 = e[m - 1], abs(r__2)) <= abs(tol) * (r__1 = d__[m], abs(
		r__1)) || tol < 0.f && (r__3 = e[m - 1], abs(r__3)) <= thresh)
		 {
	    e[m - 1] = 0.f;
	    goto L60;
	}

	if (tol >= 0.f) {

/*           If relative accuracy desired, */
/*           apply convergence criterion forward */

	    mu = (r__1 = d__[ll], abs(r__1));
	    sminl = mu;
	    i__1 = m - 1;
	    for (lll = ll; lll <= i__1; ++lll) {
		if ((r__1 = e[lll], abs(r__1)) <= tol * mu) {
		    e[lll] = 0.f;
		    goto L60;
		}
		mu = (r__2 = d__[lll + 1], abs(r__2)) * (mu / (mu + (r__1 = e[
			lll], abs(r__1))));
		sminl = f2cmin(sminl,mu);
/* L100: */
	    }
	}

    } else {

/*        Run convergence test in backward direction */
/*        First apply standard test to top of matrix */

	if ((r__2 = e[ll], abs(r__2)) <= abs(tol) * (r__1 = d__[ll], abs(r__1)
		) || tol < 0.f && (r__3 = e[ll], abs(r__3)) <= thresh) {
	    e[ll] = 0.f;
	    goto L60;
	}

	if (tol >= 0.f) {

/*           If relative accuracy desired, */
/*           apply convergence criterion backward */

	    mu = (r__1 = d__[m], abs(r__1));
	    sminl = mu;
	    i__1 = ll;
	    for (lll = m - 1; lll >= i__1; --lll) {
		if ((r__1 = e[lll], abs(r__1)) <= tol * mu) {
		    e[lll] = 0.f;
		    goto L60;
		}
		mu = (r__2 = d__[lll], abs(r__2)) * (mu / (mu + (r__1 = e[lll]
			, abs(r__1))));
		sminl = f2cmin(sminl,mu);
/* L110: */
	    }
	}
    }
    oldll = ll;
    oldm = m;

/*     Compute shift.  First, test if shifting would ruin relative */
/*     accuracy, and if so set the shift to zero. */

/* Computing MAX */
    r__1 = eps, r__2 = tol * .01f;
    if (tol >= 0.f && *n * tol * (sminl / smax) <= f2cmax(r__1,r__2)) {

/*        Use a zero shift to avoid loss of relative accuracy */

	shift = 0.f;
    } else {

/*        Compute the shift from 2-by-2 block at end of matrix */

	if (idir == 1) {
	    sll = (r__1 = d__[ll], abs(r__1));
	    slas2_(&d__[m - 1], &e[m - 1], &d__[m], &shift, &r__);
	} else {
	    sll = (r__1 = d__[m], abs(r__1));
	    slas2_(&d__[ll], &e[ll], &d__[ll + 1], &shift, &r__);
	}

/*        Test if shift negligible, and if so set to zero */

	if (sll > 0.f) {
/* Computing 2nd power */
	    r__1 = shift / sll;
	    if (r__1 * r__1 < eps) {
		shift = 0.f;
	    }
	}
    }

/*     Increment iteration count */

    iter = iter + m - ll;

/*     If SHIFT = 0, do simplified QR iteration */

    if (shift == 0.f) {
	if (idir == 1) {

/*           Chase bulge from top to bottom */
/*           Save cosines and sines for later singular vector updates */

	    cs = 1.f;
	    oldcs = 1.f;
	    i__1 = m - 1;
	    for (i__ = ll; i__ <= i__1; ++i__) {
		r__1 = d__[i__] * cs;
		slartg_(&r__1, &e[i__], &cs, &sn, &r__);
		if (i__ > ll) {
		    e[i__ - 1] = oldsn * r__;
		}
		r__1 = oldcs * r__;
		r__2 = d__[i__ + 1] * sn;
		slartg_(&r__1, &r__2, &oldcs, &oldsn, &d__[i__]);
		work[i__ - ll + 1] = cs;
		work[i__ - ll + 1 + nm1] = sn;
		work[i__ - ll + 1 + nm12] = oldcs;
		work[i__ - ll + 1 + nm13] = oldsn;
/* L120: */
	    }
	    h__ = d__[m] * cs;
	    d__[m] = h__ * oldcs;
	    e[m - 1] = h__ * oldsn;

/*           Update singular vectors */

	    if (*ncvt > 0) {
		i__1 = m - ll + 1;
		slasr_("L", "V", "F", &i__1, ncvt, &work[1], &work[*n], &vt[
			ll + vt_dim1], ldvt);
	    }
	    if (*nru > 0) {
		i__1 = m - ll + 1;
		slasr_("R", "V", "F", nru, &i__1, &work[nm12 + 1], &work[nm13 
			+ 1], &u[ll * u_dim1 + 1], ldu);
	    }
	    if (*ncc > 0) {
		i__1 = m - ll + 1;
		slasr_("L", "V", "F", &i__1, ncc, &work[nm12 + 1], &work[nm13 
			+ 1], &c__[ll + c_dim1], ldc);
	    }

/*           Test convergence */

	    if ((r__1 = e[m - 1], abs(r__1)) <= thresh) {
		e[m - 1] = 0.f;
	    }

	} else {

/*           Chase bulge from bottom to top */
/*           Save cosines and sines for later singular vector updates */

	    cs = 1.f;
	    oldcs = 1.f;
	    i__1 = ll + 1;
	    for (i__ = m; i__ >= i__1; --i__) {
		r__1 = d__[i__] * cs;
		slartg_(&r__1, &e[i__ - 1], &cs, &sn, &r__);
		if (i__ < m) {
		    e[i__] = oldsn * r__;
		}
		r__1 = oldcs * r__;
		r__2 = d__[i__ - 1] * sn;
		slartg_(&r__1, &r__2, &oldcs, &oldsn, &d__[i__]);
		work[i__ - ll] = cs;
		work[i__ - ll + nm1] = -sn;
		work[i__ - ll + nm12] = oldcs;
		work[i__ - ll + nm13] = -oldsn;
/* L130: */
	    }
	    h__ = d__[ll] * cs;
	    d__[ll] = h__ * oldcs;
	    e[ll] = h__ * oldsn;

/*           Update singular vectors */

	    if (*ncvt > 0) {
		i__1 = m - ll + 1;
		slasr_("L", "V", "B", &i__1, ncvt, &work[nm12 + 1], &work[
			nm13 + 1], &vt[ll + vt_dim1], ldvt);
	    }
	    if (*nru > 0) {
		i__1 = m - ll + 1;
		slasr_("R", "V", "B", nru, &i__1, &work[1], &work[*n], &u[ll *
			 u_dim1 + 1], ldu);
	    }
	    if (*ncc > 0) {
		i__1 = m - ll + 1;
		slasr_("L", "V", "B", &i__1, ncc, &work[1], &work[*n], &c__[
			ll + c_dim1], ldc);
	    }

/*           Test convergence */

	    if ((r__1 = e[ll], abs(r__1)) <= thresh) {
		e[ll] = 0.f;
	    }
	}
    } else {

/*        Use nonzero shift */

	if (idir == 1) {

/*           Chase bulge from top to bottom */
/*           Save cosines and sines for later singular vector updates */

	    f = ((r__1 = d__[ll], abs(r__1)) - shift) * (r_sign(&c_b49, &d__[
		    ll]) + shift / d__[ll]);
	    g = e[ll];
	    i__1 = m - 1;
	    for (i__ = ll; i__ <= i__1; ++i__) {
		slartg_(&f, &g, &cosr, &sinr, &r__);
		if (i__ > ll) {
		    e[i__ - 1] = r__;
		}
		f = cosr * d__[i__] + sinr * e[i__];
		e[i__] = cosr * e[i__] - sinr * d__[i__];
		g = sinr * d__[i__ + 1];
		d__[i__ + 1] = cosr * d__[i__ + 1];
		slartg_(&f, &g, &cosl, &sinl, &r__);
		d__[i__] = r__;
		f = cosl * e[i__] + sinl * d__[i__ + 1];
		d__[i__ + 1] = cosl * d__[i__ + 1] - sinl * e[i__];
		if (i__ < m - 1) {
		    g = sinl * e[i__ + 1];
		    e[i__ + 1] = cosl * e[i__ + 1];
		}
		work[i__ - ll + 1] = cosr;
		work[i__ - ll + 1 + nm1] = sinr;
		work[i__ - ll + 1 + nm12] = cosl;
		work[i__ - ll + 1 + nm13] = sinl;
/* L140: */
	    }
	    e[m - 1] = f;

/*           Update singular vectors */

	    if (*ncvt > 0) {
		i__1 = m - ll + 1;
		slasr_("L", "V", "F", &i__1, ncvt, &work[1], &work[*n], &vt[
			ll + vt_dim1], ldvt);
	    }
	    if (*nru > 0) {
		i__1 = m - ll + 1;
		slasr_("R", "V", "F", nru, &i__1, &work[nm12 + 1], &work[nm13 
			+ 1], &u[ll * u_dim1 + 1], ldu);
	    }
	    if (*ncc > 0) {
		i__1 = m - ll + 1;
		slasr_("L", "V", "F", &i__1, ncc, &work[nm12 + 1], &work[nm13 
			+ 1], &c__[ll + c_dim1], ldc);
	    }

/*           Test convergence */

	    if ((r__1 = e[m - 1], abs(r__1)) <= thresh) {
		e[m - 1] = 0.f;
	    }

	} else {

/*           Chase bulge from bottom to top */
/*           Save cosines and sines for later singular vector updates */

	    f = ((r__1 = d__[m], abs(r__1)) - shift) * (r_sign(&c_b49, &d__[m]
		    ) + shift / d__[m]);
	    g = e[m - 1];
	    i__1 = ll + 1;
	    for (i__ = m; i__ >= i__1; --i__) {
		slartg_(&f, &g, &cosr, &sinr, &r__);
		if (i__ < m) {
		    e[i__] = r__;
		}
		f = cosr * d__[i__] + sinr * e[i__ - 1];
		e[i__ - 1] = cosr * e[i__ - 1] - sinr * d__[i__];
		g = sinr * d__[i__ - 1];
		d__[i__ - 1] = cosr * d__[i__ - 1];
		slartg_(&f, &g, &cosl, &sinl, &r__);
		d__[i__] = r__;
		f = cosl * e[i__ - 1] + sinl * d__[i__ - 1];
		d__[i__ - 1] = cosl * d__[i__ - 1] - sinl * e[i__ - 1];
		if (i__ > ll + 1) {
		    g = sinl * e[i__ - 2];
		    e[i__ - 2] = cosl * e[i__ - 2];
		}
		work[i__ - ll] = cosr;
		work[i__ - ll + nm1] = -sinr;
		work[i__ - ll + nm12] = cosl;
		work[i__ - ll + nm13] = -sinl;
/* L150: */
	    }
	    e[ll] = f;

/*           Test convergence */

	    if ((r__1 = e[ll], abs(r__1)) <= thresh) {
		e[ll] = 0.f;
	    }

/*           Update singular vectors if desired */

	    if (*ncvt > 0) {
		i__1 = m - ll + 1;
		slasr_("L", "V", "B", &i__1, ncvt, &work[nm12 + 1], &work[
			nm13 + 1], &vt[ll + vt_dim1], ldvt);
	    }
	    if (*nru > 0) {
		i__1 = m - ll + 1;
		slasr_("R", "V", "B", nru, &i__1, &work[1], &work[*n], &u[ll *
			 u_dim1 + 1], ldu);
	    }
	    if (*ncc > 0) {
		i__1 = m - ll + 1;
		slasr_("L", "V", "B", &i__1, ncc, &work[1], &work[*n], &c__[
			ll + c_dim1], ldc);
	    }
	}
    }

/*     QR iteration finished, go back and check convergence */

    goto L60;

/*     All singular values converged, so make them positive */

L160:
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
	if (d__[i__] < 0.f) {
	    d__[i__] = -d__[i__];

/*           Change sign of singular vectors, if desired */

	    if (*ncvt > 0) {
		sscal_(ncvt, &c_b72, &vt[i__ + vt_dim1], ldvt);
	    }
	}
/* L170: */
    }

/*     Sort the singular values into decreasing order (insertion sort on */
/*     singular values, but only one transposition per singular vector) */

    i__1 = *n - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {

/*        Scan for smallest D(I) */

	isub = 1;
	smin = d__[1];
	i__2 = *n + 1 - i__;
	for (j = 2; j <= i__2; ++j) {
	    if (d__[j] <= smin) {
		isub = j;
		smin = d__[j];
	    }
/* L180: */
	}
	if (isub != *n + 1 - i__) {

/*           Swap singular values and vectors */

	    d__[isub] = d__[*n + 1 - i__];
	    d__[*n + 1 - i__] = smin;
	    if (*ncvt > 0) {
		sswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[*n + 1 - i__ + 
			vt_dim1], ldvt);
	    }
	    if (*nru > 0) {
		sswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[(*n + 1 - i__) * 
			u_dim1 + 1], &c__1);
	    }
	    if (*ncc > 0) {
		sswap_(ncc, &c__[isub + c_dim1], ldc, &c__[*n + 1 - i__ + 
			c_dim1], ldc);
	    }
	}
/* L190: */
    }
    goto L220;

/*     Maximum number of iterations exceeded, failure to converge */

L200:
    *info = 0;
    i__1 = *n - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {
	if (e[i__] != 0.f) {
	    ++(*info);
	}
/* L210: */
    }
L220:
    return;

/*     End of SBDSQR */

} /* sbdsqr_ */