OpenBLAS/lapack-netlib/SRC/clalsd.c

/* f2c.h  --  Standard Fortran to C header file */

/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."

	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */

#ifndef F2C_INCLUDE
#define F2C_INCLUDE

#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;
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;}
#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)); }
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#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) = conj(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) (cimag(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;
}
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;
}
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;
}
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;
	_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;
}
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
	_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;
}	
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
	_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;
}
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
	_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 complex c_b1 = {0.f,0.f};
static integer c__1 = 1;
static integer c__0 = 0;
static real c_b10 = 1.f;
static real c_b35 = 0.f;

/* > \brief \b CLALSD uses the singular value decomposition of A to solve the least squares problem. */

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

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

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

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

/*       SUBROUTINE CLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, */
/*                          RANK, WORK, RWORK, IWORK, INFO ) */

/*       CHARACTER          UPLO */
/*       INTEGER            INFO, LDB, N, NRHS, RANK, SMLSIZ */
/*       REAL               RCOND */
/*       INTEGER            IWORK( * ) */
/*       REAL               D( * ), E( * ), RWORK( * ) */
/*       COMPLEX            B( LDB, * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > CLALSD uses the singular value decomposition of A to solve the least */
/* > squares problem of finding X to minimize the Euclidean norm of each */
/* > column of A*X-B, where A is N-by-N upper bidiagonal, and X and B */
/* > are N-by-NRHS. The solution X overwrites B. */
/* > */
/* > The singular values of A smaller than RCOND times the largest */
/* > singular value are treated as zero in solving the least squares */
/* > problem; in this case a minimum norm solution is returned. */
/* > The actual singular values are returned in D in ascending order. */
/* > */
/* > 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. */
/* > \endverbatim */

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

/* > \param[in] UPLO */
/* > \verbatim */
/* >          UPLO is CHARACTER*1 */
/* >         = 'U': D and E define an upper bidiagonal matrix. */
/* >         = 'L': D and E define a  lower bidiagonal matrix. */
/* > \endverbatim */
/* > */
/* > \param[in] SMLSIZ */
/* > \verbatim */
/* >          SMLSIZ is INTEGER */
/* >         The maximum size of the subproblems at the bottom of the */
/* >         computation tree. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >         The dimension of the  bidiagonal matrix.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NRHS */
/* > \verbatim */
/* >          NRHS is INTEGER */
/* >         The number of columns of B. NRHS must be at least 1. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* >          D is REAL array, dimension (N) */
/* >         On entry D contains the main diagonal of the bidiagonal */
/* >         matrix. On exit, if INFO = 0, D contains its singular values. */
/* > \endverbatim */
/* > */
/* > \param[in,out] E */
/* > \verbatim */
/* >          E is REAL array, dimension (N-1) */
/* >         Contains the super-diagonal entries of the bidiagonal matrix. */
/* >         On exit, E has been destroyed. */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* >          B is COMPLEX array, dimension (LDB,NRHS) */
/* >         On input, B contains the right hand sides of the least */
/* >         squares problem. On output, B contains the solution X. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* >          LDB is INTEGER */
/* >         The leading dimension of B in the calling subprogram. */
/* >         LDB must be at least f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] RCOND */
/* > \verbatim */
/* >          RCOND is REAL */
/* >         The singular values of A less than or equal to RCOND times */
/* >         the largest singular value are treated as zero in solving */
/* >         the least squares problem. If RCOND is negative, */
/* >         machine precision is used instead. */
/* >         For example, if diag(S)*X=B were the least squares problem, */
/* >         where diag(S) is a diagonal matrix of singular values, the */
/* >         solution would be X(i) = B(i) / S(i) if S(i) is greater than */
/* >         RCOND*f2cmax(S), and X(i) = 0 if S(i) is less than or equal to */
/* >         RCOND*f2cmax(S). */
/* > \endverbatim */
/* > */
/* > \param[out] RANK */
/* > \verbatim */
/* >          RANK is INTEGER */
/* >         The number of singular values of A greater than RCOND times */
/* >         the largest singular value. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is COMPLEX array, dimension (N * NRHS). */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* >          RWORK is REAL array, dimension at least */
/* >         (9*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS + */
/* >         MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ), */
/* >         where */
/* >         NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (3*N*NLVL + 11*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:  The algorithm failed to compute a singular value while */
/* >               working on the submatrix lying in rows and columns */
/* >               INFO/(N+1) through MOD(INFO,N+1). */
/* > \endverbatim */

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

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

/* > \date December 2016 */

/* > \ingroup complexOTHERcomputational */

/* > \par Contributors: */
/*  ================== */
/* > */
/* >     Ming Gu and Ren-Cang Li, Computer Science Division, University of */
/* >       California at Berkeley, USA \n */
/* >     Osni Marques, LBNL/NERSC, USA \n */

/*  ===================================================================== */
/* Subroutine */ int clalsd_(char *uplo, integer *smlsiz, integer *n, integer 
	*nrhs, real *d__, real *e, complex *b, integer *ldb, real *rcond, 
	integer *rank, complex *work, real *rwork, integer *iwork, integer *
	info)
{
    /* System generated locals */
    integer b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, i__6;
    real r__1;
    complex q__1;

    /* Local variables */
    integer difl, difr;
    real rcnd;
    integer jcol, irwb, perm, nsub, nlvl, sqre, bxst, jrow, irwu, c__, i__, j,
	     k;
    real r__;
    integer s, u, jimag, z__, jreal;
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    integer irwib;
    extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
	    complex *, integer *);
    integer poles, sizei, irwrb, nsize;
    extern /* Subroutine */ int csrot_(integer *, complex *, integer *, 
	    complex *, integer *, real *, real *);
    integer irwvt, icmpq1, icmpq2;
    real cs;
    integer bx;
    extern /* Subroutine */ int clalsa_(integer *, integer *, integer *, 
	    integer *, complex *, integer *, complex *, integer *, real *, 
	    integer *, real *, integer *, real *, real *, real *, real *, 
	    integer *, integer *, integer *, integer *, real *, real *, real *
	    , real *, integer *, integer *);
    real sn;
    extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, complex *, integer *, integer *);
    integer st;
    extern real slamch_(char *);
    extern /* Subroutine */ int slasda_(integer *, integer *, integer *, 
	    integer *, real *, real *, real *, integer *, real *, integer *, 
	    real *, real *, real *, real *, integer *, integer *, integer *, 
	    integer *, real *, real *, real *, real *, integer *, integer *);
    integer vt;
    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
	    *, integer *, complex *, integer *), claset_(char *, 
	    integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen), slascl_(char *, 
	    integer *, integer *, real *, real *, integer *, integer *, real *
	    , integer *, integer *);
    extern integer isamax_(integer *, real *, integer *);
    integer givcol;
    extern /* Subroutine */ int slasdq_(char *, integer *, integer *, integer 
	    *, integer *, integer *, real *, real *, real *, integer *, real *
	    , integer *, real *, integer *, real *, integer *), 
	    slaset_(char *, integer *, integer *, real *, real *, real *, 
	    integer *), slartg_(real *, real *, real *, real *, real *
	    );
    real orgnrm;
    integer givnum;
    extern real slanst_(char *, integer *, real *, real *);
    extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *);
    integer givptr, nm1, nrwork, irwwrk, smlszp, st1;
    real eps;
    integer iwk;
    real tol;


/*  -- LAPACK computational 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..-- */
/*     December 2016 */


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


/*     Test the input parameters. */

    /* Parameter adjustments */
    --d__;
    --e;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --work;
    --rwork;
    --iwork;

    /* Function Body */
    *info = 0;

    if (*n < 0) {
	*info = -3;
    } else if (*nrhs < 1) {
	*info = -4;
    } else if (*ldb < 1 || *ldb < *n) {
	*info = -8;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("CLALSD", &i__1, (ftnlen)6);
	return 0;
    }

    eps = slamch_("Epsilon");

/*     Set up the tolerance. */

    if (*rcond <= 0.f || *rcond >= 1.f) {
	rcnd = eps;
    } else {
	rcnd = *rcond;
    }

    *rank = 0;

/*     Quick return if possible. */

    if (*n == 0) {
	return 0;
    } else if (*n == 1) {
	if (d__[1] == 0.f) {
	    claset_("A", &c__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
	} else {
	    *rank = 1;
	    clascl_("G", &c__0, &c__0, &d__[1], &c_b10, &c__1, nrhs, &b[
		    b_offset], ldb, info);
	    d__[1] = abs(d__[1]);
	}
	return 0;
    }

/*     Rotate the matrix if it is lower bidiagonal. */

    if (*(unsigned char *)uplo == 'L') {
	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];
	    if (*nrhs == 1) {
		csrot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], &
			c__1, &cs, &sn);
	    } else {
		rwork[(i__ << 1) - 1] = cs;
		rwork[i__ * 2] = sn;
	    }
/* L10: */
	}
	if (*nrhs > 1) {
	    i__1 = *nrhs;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		i__2 = *n - 1;
		for (j = 1; j <= i__2; ++j) {
		    cs = rwork[(j << 1) - 1];
		    sn = rwork[j * 2];
		    csrot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__ 
			    * b_dim1], &c__1, &cs, &sn);
/* L20: */
		}
/* L30: */
	    }
	}
    }

/*     Scale. */

    nm1 = *n - 1;
    orgnrm = slanst_("M", n, &d__[1], &e[1]);
    if (orgnrm == 0.f) {
	claset_("A", n, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
	return 0;
    }

    slascl_("G", &c__0, &c__0, &orgnrm, &c_b10, n, &c__1, &d__[1], n, info);
    slascl_("G", &c__0, &c__0, &orgnrm, &c_b10, &nm1, &c__1, &e[1], &nm1, 
	    info);

/*     If N is smaller than the minimum divide size SMLSIZ, then solve */
/*     the problem with another solver. */

    if (*n <= *smlsiz) {
	irwu = 1;
	irwvt = irwu + *n * *n;
	irwwrk = irwvt + *n * *n;
	irwrb = irwwrk;
	irwib = irwrb + *n * *nrhs;
	irwb = irwib + *n * *nrhs;
	slaset_("A", n, n, &c_b35, &c_b10, &rwork[irwu], n);
	slaset_("A", n, n, &c_b35, &c_b10, &rwork[irwvt], n);
	slasdq_("U", &c__0, n, n, n, &c__0, &d__[1], &e[1], &rwork[irwvt], n, 
		&rwork[irwu], n, &rwork[irwwrk], &c__1, &rwork[irwwrk], info);
	if (*info != 0) {
	    return 0;
	}

/*        In the real version, B is passed to SLASDQ and multiplied */
/*        internally by Q**H. Here B is complex and that product is */
/*        computed below in two steps (real and imaginary parts). */

	j = irwb - 1;
	i__1 = *nrhs;
	for (jcol = 1; jcol <= i__1; ++jcol) {
	    i__2 = *n;
	    for (jrow = 1; jrow <= i__2; ++jrow) {
		++j;
		i__3 = jrow + jcol * b_dim1;
		rwork[j] = b[i__3].r;
/* L40: */
	    }
/* L50: */
	}
	sgemm_("T", "N", n, nrhs, n, &c_b10, &rwork[irwu], n, &rwork[irwb], n,
		 &c_b35, &rwork[irwrb], n);
	j = irwb - 1;
	i__1 = *nrhs;
	for (jcol = 1; jcol <= i__1; ++jcol) {
	    i__2 = *n;
	    for (jrow = 1; jrow <= i__2; ++jrow) {
		++j;
		rwork[j] = r_imag(&b[jrow + jcol * b_dim1]);
/* L60: */
	    }
/* L70: */
	}
	sgemm_("T", "N", n, nrhs, n, &c_b10, &rwork[irwu], n, &rwork[irwb], n,
		 &c_b35, &rwork[irwib], n);
	jreal = irwrb - 1;
	jimag = irwib - 1;
	i__1 = *nrhs;
	for (jcol = 1; jcol <= i__1; ++jcol) {
	    i__2 = *n;
	    for (jrow = 1; jrow <= i__2; ++jrow) {
		++jreal;
		++jimag;
		i__3 = jrow + jcol * b_dim1;
		i__4 = jreal;
		i__5 = jimag;
		q__1.r = rwork[i__4], q__1.i = rwork[i__5];
		b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L80: */
	    }
/* L90: */
	}

	tol = rcnd * (r__1 = d__[isamax_(n, &d__[1], &c__1)], abs(r__1));
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    if (d__[i__] <= tol) {
		claset_("A", &c__1, nrhs, &c_b1, &c_b1, &b[i__ + b_dim1], ldb);
	    } else {
		clascl_("G", &c__0, &c__0, &d__[i__], &c_b10, &c__1, nrhs, &b[
			i__ + b_dim1], ldb, info);
		++(*rank);
	    }
/* L100: */
	}

/*        Since B is complex, the following call to SGEMM is performed */
/*        in two steps (real and imaginary parts). That is for V * B */
/*        (in the real version of the code V**H is stored in WORK). */

/*        CALL SGEMM( 'T', 'N', N, NRHS, N, ONE, WORK, N, B, LDB, ZERO, */
/*    $               WORK( NWORK ), N ) */

	j = irwb - 1;
	i__1 = *nrhs;
	for (jcol = 1; jcol <= i__1; ++jcol) {
	    i__2 = *n;
	    for (jrow = 1; jrow <= i__2; ++jrow) {
		++j;
		i__3 = jrow + jcol * b_dim1;
		rwork[j] = b[i__3].r;
/* L110: */
	    }
/* L120: */
	}
	sgemm_("T", "N", n, nrhs, n, &c_b10, &rwork[irwvt], n, &rwork[irwb], 
		n, &c_b35, &rwork[irwrb], n);
	j = irwb - 1;
	i__1 = *nrhs;
	for (jcol = 1; jcol <= i__1; ++jcol) {
	    i__2 = *n;
	    for (jrow = 1; jrow <= i__2; ++jrow) {
		++j;
		rwork[j] = r_imag(&b[jrow + jcol * b_dim1]);
/* L130: */
	    }
/* L140: */
	}
	sgemm_("T", "N", n, nrhs, n, &c_b10, &rwork[irwvt], n, &rwork[irwb], 
		n, &c_b35, &rwork[irwib], n);
	jreal = irwrb - 1;
	jimag = irwib - 1;
	i__1 = *nrhs;
	for (jcol = 1; jcol <= i__1; ++jcol) {
	    i__2 = *n;
	    for (jrow = 1; jrow <= i__2; ++jrow) {
		++jreal;
		++jimag;
		i__3 = jrow + jcol * b_dim1;
		i__4 = jreal;
		i__5 = jimag;
		q__1.r = rwork[i__4], q__1.i = rwork[i__5];
		b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L150: */
	    }
/* L160: */
	}

/*        Unscale. */

	slascl_("G", &c__0, &c__0, &c_b10, &orgnrm, n, &c__1, &d__[1], n, 
		info);
	slasrt_("D", n, &d__[1], info);
	clascl_("G", &c__0, &c__0, &orgnrm, &c_b10, n, nrhs, &b[b_offset], 
		ldb, info);

	return 0;
    }

/*     Book-keeping and setting up some constants. */

    nlvl = (integer) (log((real) (*n) / (real) (*smlsiz + 1)) / log(2.f)) + 1;

    smlszp = *smlsiz + 1;

    u = 1;
    vt = *smlsiz * *n + 1;
    difl = vt + smlszp * *n;
    difr = difl + nlvl * *n;
    z__ = difr + (nlvl * *n << 1);
    c__ = z__ + nlvl * *n;
    s = c__ + *n;
    poles = s + *n;
    givnum = poles + (nlvl << 1) * *n;
    nrwork = givnum + (nlvl << 1) * *n;
    bx = 1;

    irwrb = nrwork;
    irwib = irwrb + *smlsiz * *nrhs;
    irwb = irwib + *smlsiz * *nrhs;

    sizei = *n + 1;
    k = sizei + *n;
    givptr = k + *n;
    perm = givptr + *n;
    givcol = perm + nlvl * *n;
    iwk = givcol + (nlvl * *n << 1);

    st = 1;
    sqre = 0;
    icmpq1 = 1;
    icmpq2 = 0;
    nsub = 0;

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
	if ((r__1 = d__[i__], abs(r__1)) < eps) {
	    d__[i__] = r_sign(&eps, &d__[i__]);
	}
/* L170: */
    }

    i__1 = nm1;
    for (i__ = 1; i__ <= i__1; ++i__) {
	if ((r__1 = e[i__], abs(r__1)) < eps || i__ == nm1) {
	    ++nsub;
	    iwork[nsub] = st;

/*           Subproblem found. First determine its size and then */
/*           apply divide and conquer on it. */

	    if (i__ < nm1) {

/*              A subproblem with E(I) small for I < NM1. */

		nsize = i__ - st + 1;
		iwork[sizei + nsub - 1] = nsize;
	    } else if ((r__1 = e[i__], abs(r__1)) >= eps) {

/*              A subproblem with E(NM1) not too small but I = NM1. */

		nsize = *n - st + 1;
		iwork[sizei + nsub - 1] = nsize;
	    } else {

/*              A subproblem with E(NM1) small. This implies an */
/*              1-by-1 subproblem at D(N), which is not solved */
/*              explicitly. */

		nsize = i__ - st + 1;
		iwork[sizei + nsub - 1] = nsize;
		++nsub;
		iwork[nsub] = *n;
		iwork[sizei + nsub - 1] = 1;
		ccopy_(nrhs, &b[*n + b_dim1], ldb, &work[bx + nm1], n);
	    }
	    st1 = st - 1;
	    if (nsize == 1) {

/*              This is a 1-by-1 subproblem and is not solved */
/*              explicitly. */

		ccopy_(nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n);
	    } else if (nsize <= *smlsiz) {

/*              This is a small subproblem and is solved by SLASDQ. */

		slaset_("A", &nsize, &nsize, &c_b35, &c_b10, &rwork[vt + st1],
			 n);
		slaset_("A", &nsize, &nsize, &c_b35, &c_b10, &rwork[u + st1], 
			n);
		slasdq_("U", &c__0, &nsize, &nsize, &nsize, &c__0, &d__[st], &
			e[st], &rwork[vt + st1], n, &rwork[u + st1], n, &
			rwork[nrwork], &c__1, &rwork[nrwork], info)
			;
		if (*info != 0) {
		    return 0;
		}

/*              In the real version, B is passed to SLASDQ and multiplied */
/*              internally by Q**H. Here B is complex and that product is */
/*              computed below in two steps (real and imaginary parts). */

		j = irwb - 1;
		i__2 = *nrhs;
		for (jcol = 1; jcol <= i__2; ++jcol) {
		    i__3 = st + nsize - 1;
		    for (jrow = st; jrow <= i__3; ++jrow) {
			++j;
			i__4 = jrow + jcol * b_dim1;
			rwork[j] = b[i__4].r;
/* L180: */
		    }
/* L190: */
		}
		sgemm_("T", "N", &nsize, nrhs, &nsize, &c_b10, &rwork[u + st1]
			, n, &rwork[irwb], &nsize, &c_b35, &rwork[irwrb], &
			nsize);
		j = irwb - 1;
		i__2 = *nrhs;
		for (jcol = 1; jcol <= i__2; ++jcol) {
		    i__3 = st + nsize - 1;
		    for (jrow = st; jrow <= i__3; ++jrow) {
			++j;
			rwork[j] = r_imag(&b[jrow + jcol * b_dim1]);
/* L200: */
		    }
/* L210: */
		}
		sgemm_("T", "N", &nsize, nrhs, &nsize, &c_b10, &rwork[u + st1]
			, n, &rwork[irwb], &nsize, &c_b35, &rwork[irwib], &
			nsize);
		jreal = irwrb - 1;
		jimag = irwib - 1;
		i__2 = *nrhs;
		for (jcol = 1; jcol <= i__2; ++jcol) {
		    i__3 = st + nsize - 1;
		    for (jrow = st; jrow <= i__3; ++jrow) {
			++jreal;
			++jimag;
			i__4 = jrow + jcol * b_dim1;
			i__5 = jreal;
			i__6 = jimag;
			q__1.r = rwork[i__5], q__1.i = rwork[i__6];
			b[i__4].r = q__1.r, b[i__4].i = q__1.i;
/* L220: */
		    }
/* L230: */
		}

		clacpy_("A", &nsize, nrhs, &b[st + b_dim1], ldb, &work[bx + 
			st1], n);
	    } else {

/*              A large problem. Solve it using divide and conquer. */

		slasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], &
			rwork[u + st1], n, &rwork[vt + st1], &iwork[k + st1], 
			&rwork[difl + st1], &rwork[difr + st1], &rwork[z__ + 
			st1], &rwork[poles + st1], &iwork[givptr + st1], &
			iwork[givcol + st1], n, &iwork[perm + st1], &rwork[
			givnum + st1], &rwork[c__ + st1], &rwork[s + st1], &
			rwork[nrwork], &iwork[iwk], info);
		if (*info != 0) {
		    return 0;
		}
		bxst = bx + st1;
		clalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b[st + b_dim1], ldb, &
			work[bxst], n, &rwork[u + st1], n, &rwork[vt + st1], &
			iwork[k + st1], &rwork[difl + st1], &rwork[difr + st1]
			, &rwork[z__ + st1], &rwork[poles + st1], &iwork[
			givptr + st1], &iwork[givcol + st1], n, &iwork[perm + 
			st1], &rwork[givnum + st1], &rwork[c__ + st1], &rwork[
			s + st1], &rwork[nrwork], &iwork[iwk], info);
		if (*info != 0) {
		    return 0;
		}
	    }
	    st = i__ + 1;
	}
/* L240: */
    }

/*     Apply the singular values and treat the tiny ones as zero. */

    tol = rcnd * (r__1 = d__[isamax_(n, &d__[1], &c__1)], abs(r__1));

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

/*        Some of the elements in D can be negative because 1-by-1 */
/*        subproblems were not solved explicitly. */

	if ((r__1 = d__[i__], abs(r__1)) <= tol) {
	    claset_("A", &c__1, nrhs, &c_b1, &c_b1, &work[bx + i__ - 1], n);
	} else {
	    ++(*rank);
	    clascl_("G", &c__0, &c__0, &d__[i__], &c_b10, &c__1, nrhs, &work[
		    bx + i__ - 1], n, info);
	}
	d__[i__] = (r__1 = d__[i__], abs(r__1));
/* L250: */
    }

/*     Now apply back the right singular vectors. */

    icmpq2 = 1;
    i__1 = nsub;
    for (i__ = 1; i__ <= i__1; ++i__) {
	st = iwork[i__];
	st1 = st - 1;
	nsize = iwork[sizei + i__ - 1];
	bxst = bx + st1;
	if (nsize == 1) {
	    ccopy_(nrhs, &work[bxst], n, &b[st + b_dim1], ldb);
	} else if (nsize <= *smlsiz) {

/*           Since B and BX are complex, the following call to SGEMM */
/*           is performed in two steps (real and imaginary parts). */

/*           CALL SGEMM( 'T', 'N', NSIZE, NRHS, NSIZE, ONE, */
/*    $                  RWORK( VT+ST1 ), N, RWORK( BXST ), N, ZERO, */
/*    $                  B( ST, 1 ), LDB ) */

	    j = bxst - *n - 1;
	    jreal = irwb - 1;
	    i__2 = *nrhs;
	    for (jcol = 1; jcol <= i__2; ++jcol) {
		j += *n;
		i__3 = nsize;
		for (jrow = 1; jrow <= i__3; ++jrow) {
		    ++jreal;
		    i__4 = j + jrow;
		    rwork[jreal] = work[i__4].r;
/* L260: */
		}
/* L270: */
	    }
	    sgemm_("T", "N", &nsize, nrhs, &nsize, &c_b10, &rwork[vt + st1], 
		    n, &rwork[irwb], &nsize, &c_b35, &rwork[irwrb], &nsize);
	    j = bxst - *n - 1;
	    jimag = irwb - 1;
	    i__2 = *nrhs;
	    for (jcol = 1; jcol <= i__2; ++jcol) {
		j += *n;
		i__3 = nsize;
		for (jrow = 1; jrow <= i__3; ++jrow) {
		    ++jimag;
		    rwork[jimag] = r_imag(&work[j + jrow]);
/* L280: */
		}
/* L290: */
	    }
	    sgemm_("T", "N", &nsize, nrhs, &nsize, &c_b10, &rwork[vt + st1], 
		    n, &rwork[irwb], &nsize, &c_b35, &rwork[irwib], &nsize);
	    jreal = irwrb - 1;
	    jimag = irwib - 1;
	    i__2 = *nrhs;
	    for (jcol = 1; jcol <= i__2; ++jcol) {
		i__3 = st + nsize - 1;
		for (jrow = st; jrow <= i__3; ++jrow) {
		    ++jreal;
		    ++jimag;
		    i__4 = jrow + jcol * b_dim1;
		    i__5 = jreal;
		    i__6 = jimag;
		    q__1.r = rwork[i__5], q__1.i = rwork[i__6];
		    b[i__4].r = q__1.r, b[i__4].i = q__1.i;
/* L300: */
		}
/* L310: */
	    }
	} else {
	    clalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b[st + 
		    b_dim1], ldb, &rwork[u + st1], n, &rwork[vt + st1], &
		    iwork[k + st1], &rwork[difl + st1], &rwork[difr + st1], &
		    rwork[z__ + st1], &rwork[poles + st1], &iwork[givptr + 
		    st1], &iwork[givcol + st1], n, &iwork[perm + st1], &rwork[
		    givnum + st1], &rwork[c__ + st1], &rwork[s + st1], &rwork[
		    nrwork], &iwork[iwk], info);
	    if (*info != 0) {
		return 0;
	    }
	}
/* L320: */
    }

/*     Unscale and sort the singular values. */

    slascl_("G", &c__0, &c__0, &c_b10, &orgnrm, n, &c__1, &d__[1], n, info);
    slasrt_("D", n, &d__[1], info);
    clascl_("G", &c__0, &c__0, &orgnrm, &c_b10, n, nrhs, &b[b_offset], ldb, 
	    info);

    return 0;

/*     End of CLALSD */

} /* clalsd_ */