#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 */

};

typedef struct Vardesc Vardesc;

struct Namelist {

};

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 complex c_b1 = {0.f,0.f};

static integer c__9 = 9;

static integer c__0 = 0;

static integer c__6 = 6;

static integer c_n1 = -1;

static integer c__1 = 1;

static real c_b80 = 0.f;

/* > \brief <b> CGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices</b

> */

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

/* Online html documentation available at */

/* http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */

/* > Download CGELSD + dependencies */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgelsd.

f"> */

/* > [TGZ]</a> */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgelsd.

f"> */

/* > [ZIP]</a> */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgelsd.

f"> */

/* > [TXT]</a> */

/* > \endhtmlonly */

/* Definition: */

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

/* SUBROUTINE CGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, */

/* WORK, LWORK, RWORK, IWORK, INFO ) */

/* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */

/* REAL RCOND */

/* INTEGER IWORK( * ) */

/* REAL RWORK( * ), S( * ) */

/* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > CGELSD computes the minimum-norm solution to a real linear least */

/* > squares problem: */

/* > minimize 2-norm(| b - A*x |) */

/* > using the singular value decomposition (SVD) of A. A is an M-by-N */

/* > matrix which may be rank-deficient. */

/* > */

/* > Several right hand side vectors b and solution vectors x can be */

/* > handled in a single call; they are stored as the columns of the */

/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */

/* > matrix X. */

/* > */

/* > The problem is solved in three steps: */

/* > (1) Reduce the coefficient matrix A to bidiagonal form with */

/* > Householder transformations, reducing the original problem */

/* > into a "bidiagonal least squares problem" (BLS) */

/* > (2) Solve the BLS using a divide and conquer approach. */

/* > (3) Apply back all the Householder transformations to solve */

/* > the original least squares problem. */

/* > */

/* > The effective rank of A is determined by treating as zero those */

/* > singular values which are less than RCOND times the largest singular */

/* > value. */

/* > */

/* > The divide and conquer algorithm 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 X-MP, Cray Y-MP, 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] M */

/* > \verbatim */

/* > M is INTEGER */

/* > The number of rows of the matrix A. M >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* > N is INTEGER */

/* > The number of columns of the matrix A. N >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in] NRHS */

/* > \verbatim */

/* > NRHS is INTEGER */

/* > The number of right hand sides, i.e., the number of columns */

/* > of the matrices B and X. NRHS >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in,out] A */

/* > \verbatim */

/* > A is COMPLEX array, dimension (LDA,N) */

/* > On entry, the M-by-N matrix A. */

/* > On exit, A has been destroyed. */

/* > \endverbatim */

/* > */

/* > \param[in] LDA */

/* > \verbatim */

/* > LDA is INTEGER */

/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */

/* > \endverbatim */

/* > */

/* > \param[in,out] B */

/* > \verbatim */

/* > B is COMPLEX array, dimension (LDB,NRHS) */

/* > On entry, the M-by-NRHS right hand side matrix B. */

/* > On exit, B is overwritten by the N-by-NRHS solution matrix X. */

/* > If m >= n and RANK = n, the residual sum-of-squares for */

/* > the solution in the i-th column is given by the sum of */

/* > squares of the modulus of elements n+1:m in that column. */

/* > \endverbatim */

/* > */

/* > \param[in] LDB */

/* > \verbatim */

/* > LDB is INTEGER */

/* > The leading dimension of the array B. LDB >= f2cmax(1,M,N). */

/* > \endverbatim */

/* > */

/* > \param[out] S */

/* > \verbatim */

/* > S is REAL array, dimension (f2cmin(M,N)) */

/* > The singular values of A in decreasing order. */

/* > The condition number of A in the 2-norm = S(1)/S(f2cmin(m,n)). */

/* > \endverbatim */

/* > */

/* > \param[in] RCOND */

/* > \verbatim */

/* > RCOND is REAL */

/* > RCOND is used to determine the effective rank of A. */

/* > Singular values S(i) <= RCOND*S(1) are treated as zero. */

/* > If RCOND < 0, machine precision is used instead. */

/* > \endverbatim */

/* > */

/* > \param[out] RANK */

/* > \verbatim */

/* > RANK is INTEGER */

/* > The effective rank of A, i.e., the number of singular values */

/* > which are greater than RCOND*S(1). */

/* > \endverbatim */

/* > */

/* > \param[out] WORK */

/* > \verbatim */

/* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */

/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

/* > \endverbatim */

/* > */

/* > \param[in] LWORK */

/* > \verbatim */

/* > LWORK is INTEGER */

/* > The dimension of the array WORK. LWORK must be at least 1. */

/* > The exact minimum amount of workspace needed depends on M, */

/* > N and NRHS. As long as LWORK is at least */

/* > 2 * N + N * NRHS */

/* > if M is greater than or equal to N or */

/* > 2 * M + M * NRHS */

/* > if M is less than N, the code will execute correctly. */

/* > For good performance, LWORK should generally be larger. */

/* > */

/* > If LWORK = -1, then a workspace query is assumed; the routine */

/* > only calculates the optimal size of the array WORK and the */

/* > minimum sizes of the arrays RWORK and IWORK, and returns */

/* > these values as the first entries of the WORK, RWORK and */

/* > IWORK arrays, and no error message related to LWORK is issued */

/* > by XERBLA. */

/* > \endverbatim */

/* > */

/* > \param[out] RWORK */

/* > \verbatim */

/* > RWORK is REAL array, dimension (MAX(1,LRWORK)) */

/* > LRWORK >= */

/* > 10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS + */

/* > MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ) */

/* > if M is greater than or equal to N or */

/* > 10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS + */

/* > MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ) */

/* > if M is less than N, the code will execute correctly. */

/* > SMLSIZ is returned by ILAENV and is equal to the maximum */

/* > size of the subproblems at the bottom of the computation */

/* > tree (usually about 25), and */

/* > NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) */

/* > On exit, if INFO = 0, RWORK(1) returns the minimum LRWORK. */

/* > \endverbatim */

/* > */

/* > \param[out] IWORK */

/* > \verbatim */

/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */

/* > LIWORK >= f2cmax(1, 3*MINMN*NLVL + 11*MINMN), */

/* > where MINMN = MIN( M,N ). */

/* > On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK. */

/* > \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 for computing the SVD failed to converge; */

/* > if INFO = i, i off-diagonal elements of an intermediate */

/* > bidiagonal form did not converge to zero. */

/* > \endverbatim */

/* Authors: */

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

/* > \author Univ. of Tennessee */

/* > \author Univ. of California Berkeley */

/* > \author Univ. of Colorado Denver */

/* > \author NAG Ltd. */

/* > \date December 2016 */

/* > \ingroup complexGEsolve */

/* > \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 */ void cgelsd_(integer *m, integer *n, integer *nrhs, complex *

a, integer *lda, complex *b, integer *ldb, real *s, real *rcond,

integer *rank, complex *work, integer *lwork, real *rwork, integer *

iwork, integer *info)

{

/* System generated locals */

integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;

/* Local variables */

real anrm, bnrm;

integer itau, nlvl, iascl, ibscl;

real sfmin;

integer minmn, maxmn, itaup, itauq, mnthr, nwork, ie, il;

extern /* Subroutine */ void cgebrd_(integer *, integer *, complex *,

integer *, real *, real *, complex *, complex *, complex *,

integer *, integer *), slabad_(real *, real *);

extern real clange_(char *, integer *, integer *, complex *, integer *,

real *);

integer mm;

extern /* Subroutine */ void cgelqf_(integer *, integer *, complex *,

integer *, complex *, complex *, integer *, integer *), clalsd_(

char *, integer *, integer *, integer *, real *, real *, complex *

, integer *, real *, integer *, complex *, real *, integer *,

integer *), clascl_(char *, integer *, integer *, real *,

real *, integer *, integer *, complex *, integer *, integer *), cgeqrf_(integer *, integer *, complex *, integer *,

complex *, complex *, integer *, integer *);

extern real slamch_(char *);

extern /* Subroutine */ void clacpy_(char *, integer *, integer *, complex

*, integer *, complex *, integer *), claset_(char *,

integer *, integer *, complex *, complex *, complex *, integer *);

extern int xerbla_(char *, integer *, ftnlen);

extern integer ilaenv_(integer *, char *, char *, integer *, integer *,

integer *, integer *, ftnlen, ftnlen);

real bignum;

extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *,

real *, integer *, integer *, real *, integer *, integer *), cunmbr_(char *, char *, char *, integer *, integer *,

integer *, complex *, integer *, complex *, complex *, integer *,

complex *, integer *, integer *), slaset_(

char *, integer *, integer *, real *, real *, real *, integer *), cunmlq_(char *, char *, integer *, integer *, integer *,

complex *, integer *, complex *, complex *, integer *, complex *,

integer *, integer *);

integer ldwork;

extern /* Subroutine */ void cunmqr_(char *, char *, integer *, integer *,

integer *, complex *, integer *, complex *, complex *, integer *,

complex *, integer *, integer *);

integer liwork, minwrk, maxwrk;

real smlnum;

integer lrwork;

logical lquery;

integer nrwork, smlsiz;

real eps;

/* -- LAPACK driver 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 arguments. */

/* Parameter adjustments */

a_dim1 = *lda;

a_offset = 1 + a_dim1 * 1;

a -= a_offset;

b_dim1 = *ldb;

b_offset = 1 + b_dim1 * 1;

b -= b_offset;

--s;

--work;

--rwork;

--iwork;

/* Function Body */

*info = 0;

minmn = f2cmin(*m,*n);

maxmn = f2cmax(*m,*n);

lquery = *lwork == -1;

if (*m < 0) {

*info = -1;

} else if (*n < 0) {

*info = -2;

} else if (*nrhs < 0) {

*info = -3;

} else if (*lda < f2cmax(1,*m)) {

*info = -5;

} else if (*ldb < f2cmax(1,maxmn)) {

*info = -7;

}

/* Compute workspace. */

/* (Note: Comments in the code beginning "Workspace:" describe the */

/* minimal amount of workspace needed at that point in the code, */

/* as well as the preferred amount for good performance. */

/* NB refers to the optimal block size for the immediately */

/* following subroutine, as returned by ILAENV.) */

if (*info == 0) {

minwrk = 1;

maxwrk = 1;

liwork = 1;

lrwork = 1;

if (minmn > 0) {

smlsiz = ilaenv_(&c__9, "CGELSD", " ", &c__0, &c__0, &c__0, &c__0,

(ftnlen)6, (ftnlen)1);

mnthr = ilaenv_(&c__6, "CGELSD", " ", m, n, nrhs, &c_n1, (ftnlen)

6, (ftnlen)1);

/* Computing MAX */

i__1 = (integer) (log((real) minmn / (real) (smlsiz + 1)) / log(

2.f)) + 1;

nlvl = f2cmax(i__1,0);

liwork = minmn * 3 * nlvl + minmn * 11;

mm = *m;

if (*m >= *n && *m >= mnthr) {

/* Path 1a - overdetermined, with many more rows than */

/* columns. */

mm = *n;

/* Computing MAX */

i__1 = maxwrk, i__2 = *n * ilaenv_(&c__1, "CGEQRF", " ", m, n,

&c_n1, &c_n1, (ftnlen)6, (ftnlen)1);

maxwrk = f2cmax(i__1,i__2);

/* Computing MAX */

i__1 = maxwrk, i__2 = *nrhs * ilaenv_(&c__1, "CUNMQR", "LC",

m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2);

maxwrk = f2cmax(i__1,i__2);

}

if (*m >= *n) {

/* Path 1 - overdetermined or exactly determined. */

/* Computing MAX */

/* Computing 2nd power */

i__3 = smlsiz + 1;

i__1 = i__3 * i__3, i__2 = *n * (*nrhs + 1) + (*nrhs << 1);

lrwork = *n * 10 + (*n << 1) * smlsiz + (*n << 3) * nlvl +

smlsiz * 3 * *nrhs + f2cmax(i__1,i__2);

/* Computing MAX */

i__1 = maxwrk, i__2 = (*n << 1) + (mm + *n) * ilaenv_(&c__1,

"CGEBRD", " ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (

ftnlen)1);

maxwrk = f2cmax(i__1,i__2);

/* Computing MAX */

i__1 = maxwrk, i__2 = (*n << 1) + *nrhs * ilaenv_(&c__1,

"CUNMBR", "QLC", &mm, nrhs, n, &c_n1, (ftnlen)6, (

ftnlen)3);

maxwrk = f2cmax(i__1,i__2);

/* Computing MAX */

i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1,

"CUNMBR", "PLN", n, nrhs, n, &c_n1, (ftnlen)6, (

ftnlen)3);

maxwrk = f2cmax(i__1,i__2);

/* Computing MAX */

i__1 = maxwrk, i__2 = (*n << 1) + *n * *nrhs;

maxwrk = f2cmax(i__1,i__2);

/* Computing MAX */

i__1 = (*n << 1) + mm, i__2 = (*n << 1) + *n * *nrhs;

minwrk = f2cmax(i__1,i__2);

}

if (*n > *m) {

/* Computing MAX */

/* Computing 2nd power */

i__3 = smlsiz + 1;

i__1 = i__3 * i__3, i__2 = *n * (*nrhs + 1) + (*nrhs << 1);

lrwork = *m * 10 + (*m << 1) * smlsiz + (*m << 3) * nlvl +

smlsiz * 3 * *nrhs + f2cmax(i__1,i__2);

if (*n >= mnthr) {

/* Path 2a - underdetermined, with many more columns */

/* than rows. */

maxwrk = *m + *m * ilaenv_(&c__1, "CGELQF", " ", m, n, &

c_n1, &c_n1, (ftnlen)6, (ftnlen)1);

/* Computing MAX */

i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) *

ilaenv_(&c__1, "CGEBRD", " ", m, m, &c_n1, &c_n1,

(ftnlen)6, (ftnlen)1);

maxwrk = f2cmax(i__1,i__2);

/* Computing MAX */

i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs *

ilaenv_(&c__1, "CUNMBR", "QLC", m, nrhs, m, &c_n1,

(ftnlen)6, (ftnlen)3);

maxwrk = f2cmax(i__1,i__2);

/* Computing MAX */

i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) *

ilaenv_(&c__1, "CUNMLQ", "LC", n, nrhs, m, &c_n1,

(ftnlen)6, (ftnlen)2);

maxwrk = f2cmax(i__1,i__2);

if (*nrhs > 1) {

/* Computing MAX */

i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;

maxwrk = f2cmax(i__1,i__2);

} else {

/* Computing MAX */

i__1 = maxwrk, i__2 = *m * *m + (*m << 1);

maxwrk = f2cmax(i__1,i__2);

}

/* Computing MAX */

i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *m * *nrhs;

maxwrk = f2cmax(i__1,i__2);

/* XXX: Ensure the Path 2a case below is triggered. The workspace */

/* calculation should use queries for all routines eventually. */

/* Computing MAX */

/* Computing MAX */

i__3 = *m, i__4 = (*m << 1) - 4, i__3 = f2cmax(i__3,i__4),

i__3 = f2cmax(i__3,*nrhs), i__4 = *n - *m * 3;

i__1 = maxwrk, i__2 = (*m << 2) + *m * *m + f2cmax(i__3,i__4)

;

maxwrk = f2cmax(i__1,i__2);

} else {

/* Path 2 - underdetermined. */

maxwrk = (*m << 1) + (*n + *m) * ilaenv_(&c__1, "CGEBRD",

" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);

/* Computing MAX */

i__1 = maxwrk, i__2 = (*m << 1) + *nrhs * ilaenv_(&c__1,

"CUNMBR", "QLC", m, nrhs, m, &c_n1, (ftnlen)6, (

ftnlen)3);

maxwrk = f2cmax(i__1,i__2);

/* Computing MAX */

i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1,

"CUNMBR", "PLN", n, nrhs, m, &c_n1, (ftnlen)6, (

ftnlen)3);

maxwrk = f2cmax(i__1,i__2);

/* Computing MAX */

i__1 = maxwrk, i__2 = (*m << 1) + *m * *nrhs;

maxwrk = f2cmax(i__1,i__2);

}

/* Computing MAX */

i__1 = (*m << 1) + *n, i__2 = (*m << 1) + *m * *nrhs;

minwrk = f2cmax(i__1,i__2);

}

}

minwrk = f2cmin(minwrk,maxwrk);

work[1].r = (real) maxwrk, work[1].i = 0.f;

iwork[1] = liwork;

rwork[1] = (real) lrwork;

if (*lwork < minwrk && ! lquery) {

*info = -12;

}

}

if (*info != 0) {

i__1 = -(*info);

xerbla_("CGELSD", &i__1, (ftnlen)6);

return;

} else if (lquery) {

return;