cgelsy.c

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

#if defined(_WIN64)
typedeflong longBLASLONG;
typedefunsigned long longBLASULONG;
#else
typedeflongBLASLONG;
typedefunsigned longBLASULONG;
#endif

#ifdefLAPACK_ILP64
typedefBLASLONGblasint;
#if defined(_WIN64)
#defineblasabs(x) llabs(x)
#else
#defineblasabs(x) labs(x)
#endif
#else
typedefintblasint;
#defineblasabs(x) abs(x)
#endif

typedefblasintinteger;

typedefunsigned intuinteger;
typedefchar*address;
typedefshort intshortint;
typedeffloatreal;
typedefdoubledoublereal;
typedefstruct { realr, i; } complex;
typedefstruct { doublerealr, i; } doublecomplex;
#ifdef_MSC_VER
staticinline_FcomplexCf(complex*z) {_Fcomplexzz={z->r , z->i}; returnzz;}
staticinline_DcomplexCd(doublecomplex*z) {_Dcomplexzz={z->r , z->i};returnzz;}
staticinline_Fcomplex*_pCf(complex*z) {return (_Fcomplex*)z;}
staticinline_Dcomplex*_pCd(doublecomplex*z) {return (_Dcomplex*)z;}
#else
staticinline_ComplexfloatCf(complex*z) {returnz->r+z->i*_Complex_I;}
staticinline_ComplexdoubleCd(doublecomplex*z) {returnz->r+z->i*_Complex_I;}
staticinline_Complexfloat*_pCf(complex*z) {return (_Complexfloat*)z;}
staticinline_Complexdouble*_pCd(doublecomplex*z) {return (_Complexdouble*)z;}
#endif
#definepCf(z) (*_pCf(z))
#definepCd(z) (*_pCd(z))
typedefintlogical;
typedefshort intshortlogical;
typedefcharlogical1;
typedefcharinteger1;

#defineTRUE_ (1)
#defineFALSE_ (0)

/* Extern is for use with -E */
#ifndefExtern
#defineExtern extern
#endif

/* I/O stuff */

typedefintflag;
typedefintftnlen;
typedefintftnint;

/*external read, write*/
typedefstruct
{ flagcierr;
ftnintciunit;
flagciend;
char*cifmt;
ftnintcirec;
} cilist;

/*internal read, write*/
typedefstruct
{ flagicierr;
char*iciunit;
flagiciend;
char*icifmt;
ftninticirlen;
ftninticirnum;
} icilist;

/*open*/
typedefstruct
{ flagoerr;
ftnintounit;
char*ofnm;
ftnlenofnmlen;
char*osta;
char*oacc;
char*ofm;
ftnintorl;
char*oblnk;
} olist;

/*close*/
typedefstruct
{ flagcerr;
ftnintcunit;
char*csta;
} cllist;

/*rewind, backspace, endfile*/
typedefstruct
{ flagaerr;
ftnintaunit;
} alist;

/* inquire */
typedefstruct
{ flaginerr;
ftnintinunit;
char*infile;
ftnleninfilen;
ftnint*inex; /*parameters in standard's order*/
ftnint*inopen;
ftnint*innum;
ftnint*innamed;
char*inname;
ftnleninnamlen;
char*inacc;
ftnleninacclen;
char*inseq;
ftnleninseqlen;
char*indir;
ftnlenindirlen;
char*infmt;
ftnleninfmtlen;
char*inform;
ftnintinformlen;
char*inunf;
ftnleninunflen;
ftnint*inrecl;
ftnint*innrec;
char*inblank;
ftnleninblanklen;
} inlist;

#defineVOID void

unionMultitype { /* for multiple entry points */
integer1g;
shortinth;
integeri;
/* longint j; */
realr;
doublereald;
complexc;
doublecomplexz;
 };

typedefunionMultitypeMultitype;

structVardesc { /* for Namelist */
char*name;
char*addr;
ftnlen*dims;
inttype;
 };
typedefstructVardescVardesc;

structNamelist {
char*name;
Vardesc**vars;
intnvars;
 };
typedefstructNamelistNamelist;

#defineabs(x) ((x) >= 0 ? (x) : -(x))
#definedabs(x) (fabs(x))
#definef2cmin(a,b) ((a) <= (b) ? (a) : (b))
#definef2cmax(a,b) ((a) >= (b) ? (a) : (b))
#definedmin(a,b) (f2cmin(a,b))
#definedmax(a,b) (f2cmax(a,b))
#definebit_test(a,b) ((a) >> (b) & 1)
#definebit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#definebit_set(a,b) ((a) | ((uinteger)1 << (b)))

#defineabort_() { sig_die("Fortran abort routine called", 1); }
#definec_abs(z) (cabsf(Cf(z)))
#definec_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef_MSC_VER
#definec_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]);}
#definez_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
#definec_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#definez_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#definec_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#definec_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#definec_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#definec_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#defined_abs(x) (fabs(*(x)))
#defined_acos(x) (acos(*(x)))
#defined_asin(x) (asin(*(x)))
#defined_atan(x) (atan(*(x)))
#defined_atn2(x, y) (atan2(*(x),*(y)))
#defined_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#definer_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#defined_cos(x) (cos(*(x)))
#defined_cosh(x) (cosh(*(x)))
#defined_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#defined_exp(x) (exp(*(x)))
#defined_imag(z) (cimag(Cd(z)))
#definer_imag(z) (cimagf(Cf(z)))
#defined_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#definer_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#defined_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#definer_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#defined_log(x) (log(*(x)))
#defined_mod(x, y) (fmod(*(x), *(y)))
#defineu_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#defined_nint(x) u_nint(*(x))
#defineu_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#defined_sign(a,b) u_sign(*(a),*(b))
#definer_sign(a,b) u_sign(*(a),*(b))
#defined_sin(x) (sin(*(x)))
#defined_sinh(x) (sinh(*(x)))
#defined_sqrt(x) (sqrt(*(x)))
#defined_tan(x) (tan(*(x)))
#defined_tanh(x) (tanh(*(x)))
#definei_abs(x) abs(*(x))
#definei_dnnt(x) ((integer)u_nint(*(x)))
#definei_len(s, n) (n)
#definei_nint(x) ((integer)u_nint(*(x)))
#definei_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#definepow_dd(ap, bp) ( pow(*(ap), *(bp)))
#definepow_si(B,E) spow_ui(*(B),*(E))
#definepow_ri(B,E) spow_ui(*(B),*(E))
#definepow_di(B,E) dpow_ui(*(B),*(E))
#definepow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#definepow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#definepow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#defines_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++ = ' '; }
#defines_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#defines_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]; }
#definesig_die(s, kill) { exit(1); }
#defines_stop(s, n) {exit(0);}
staticcharjunk[] ="\n@(#)LIBF77 VERSION 19990503\n";
#definez_abs(z) (cabs(Cd(z)))
#definez_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#definez_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#definemyexit_() break;
#definemycycle() continue;
#definemyceiling(w) {ceil(w)}
#definemyhuge(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);}
#definemymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}

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

#defineF2C_proc_par_types 1
#ifdef__cplusplus
typedeflogical (*L_fp)(...);
#else
typedeflogical (*L_fp)();
#endif

staticfloatspow_ui(floatx, integern) {
floatpow=1.0; unsigned long intu;
if(n!=0) {
if(n<0) n=-n, x=1/x;
for(u=n; ; ) {
if(u&01) pow *= x;
if(u >>= 1) x *= x;
elsebreak;
 }
 }
returnpow;
}
staticdoubledpow_ui(doublex, integern) {
doublepow=1.0; unsigned long intu;
if(n!=0) {
if(n<0) n=-n, x=1/x;
for(u=n; ; ) {
if(u&01) pow *= x;
if(u >>= 1) x *= x;
elsebreak;
 }
 }
returnpow;
}
#ifdef_MSC_VER
static_Fcomplexcpow_ui(complexx, integern) {
complexpow={1.0,0.0}; unsigned long intu;
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;
elsebreak;
 }
 }
_Fcomplexp={pow.r, pow.i};
returnp;
}
#else
static_Complexfloatcpow_ui(_Complexfloatx, integern) {
_Complexfloatpow=1.0; unsigned long intu;
if(n!=0) {
if(n<0) n=-n, x=1/x;
for(u=n; ; ) {
if(u&01) pow *= x;
if(u >>= 1) x *= x;
elsebreak;
 }
 }
returnpow;
}
#endif
#ifdef_MSC_VER
static_Dcomplexzpow_ui(_Dcomplexx, integern) {
_Dcomplexpow={1.0,0.0}; unsigned long intu;
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];
elsebreak;
 }
 }
_Dcomplexp= {pow._Val[0], pow._Val[1]};
returnp;
}
#else
static_Complexdoublezpow_ui(_Complexdoublex, integern) {
_Complexdoublepow=1.0; unsigned long intu;
if(n!=0) {
if(n<0) n=-n, x=1/x;
for(u=n; ; ) {
if(u&01) pow *= x;
if(u >>= 1) x *= x;
elsebreak;
 }
 }
returnpow;
}
#endif
staticintegerpow_ii(integerx, integern) {
integerpow; unsigned long intu;
if (n <= 0) {
if (n==0||x==1) pow=1;
elseif (x!=-1) pow=x==0 ? 1/x : 0;
elsen=-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;
elsebreak;
 }
 }
returnpow;
}
staticintegerdmaxloc_(double*w, integers, integere, integer*n)
{
doublem; integeri, 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];
returnmi-s+1;
}
staticintegersmaxloc_(float*w, integers, integere, integer*n)
{
floatm; integeri, 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];
returnmi-s+1;
}
staticinlinevoidcdotc_(complex*z, integer*n_, complex*x, integer*incx_, complex*y, integer*incy_) {
integern=*n_, incx=*incx_, incy=*incy_, i;
#ifdef_MSC_VER
_Fcomplexzdotc= {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
_Complexfloatzdotc=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
staticinlinevoidzdotc_(doublecomplex*z, integer*n_, doublecomplex*x, integer*incx_, doublecomplex*y, integer*incy_) {
integern=*n_, incx=*incx_, incy=*incy_, i;
#ifdef_MSC_VER
_Dcomplexzdotc= {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
_Complexdoublezdotc=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
staticinlinevoidcdotu_(complex*z, integer*n_, complex*x, integer*incx_, complex*y, integer*incy_) {
integern=*n_, incx=*incx_, incy=*incy_, i;
#ifdef_MSC_VER
_Fcomplexzdotc= {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
_Complexfloatzdotc=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
staticinlinevoidzdotu_(doublecomplex*z, integer*n_, doublecomplex*x, integer*incx_, doublecomplex*y, integer*incy_) {
integern=*n_, incx=*incx_, incy=*incy_, i;
#ifdef_MSC_VER
_Dcomplexzdotc= {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
_Complexdoublezdotc=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 */

staticcomplexc_b1= {0.f,0.f};
staticcomplexc_b2= {1.f,0.f};
staticintegerc__1=1;
staticintegerc_n1=-1;
staticintegerc__0=0;
staticintegerc__2=2;

/* > \brief <b> CGELSY solves overdetermined or underdetermined systems for GE matrices</b> */

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

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

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

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

/* SUBROUTINE CGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, */
/* WORK, LWORK, RWORK, INFO ) */

/* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */
/* REAL RCOND */
/* INTEGER JPVT( * ) */
/* REAL RWORK( * ) */
/* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) */


/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CGELSY computes the minimum-norm solution to a complex linear least */
/* > squares problem: */
/* > minimize || A * X - B || */
/* > using a complete orthogonal factorization 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 routine first computes a QR factorization with column pivoting: */
/* > A * P = Q * [ R11 R12 ] */
/* > [ 0 R22 ] */
/* > with R11 defined as the largest leading submatrix whose estimated */
/* > condition number is less than 1/RCOND. The order of R11, RANK, */
/* > is the effective rank of A. */
/* > */
/* > Then, R22 is considered to be negligible, and R12 is annihilated */
/* > by unitary transformations from the right, arriving at the */
/* > complete orthogonal factorization: */
/* > A * P = Q * [ T11 0 ] * Z */
/* > [ 0 0 ] */
/* > The minimum-norm solution is then */
/* > X = P * Z**H [ inv(T11)*Q1**H*B ] */
/* > [ 0 ] */
/* > where Q1 consists of the first RANK columns of Q. */
/* > */
/* > This routine is basically identical to the original xGELSX except */
/* > three differences: */
/* > o The permutation of matrix B (the right hand side) is faster and */
/* > more simple. */
/* > o The call to the subroutine xGEQPF has been substituted by the */
/* > the call to the subroutine xGEQP3. This subroutine is a Blas-3 */
/* > version of the QR factorization with column pivoting. */
/* > o Matrix B (the right hand side) is updated with Blas-3. */
/* > \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 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 overwritten by details of its */
/* > complete orthogonal factorization. */
/* > \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, the N-by-NRHS solution matrix X. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of the array B. LDB >= f2cmax(1,M,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] JPVT */
/* > \verbatim */
/* > JPVT is INTEGER array, dimension (N) */
/* > On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted */
/* > to the front of AP, otherwise column i is a free column. */
/* > On exit, if JPVT(i) = k, then the i-th column of A*P */
/* > was the k-th column of A. */
/* > \endverbatim */
/* > */
/* > \param[in] RCOND */
/* > \verbatim */
/* > RCOND is REAL */
/* > RCOND is used to determine the effective rank of A, which */
/* > is defined as the order of the largest leading triangular */
/* > submatrix R11 in the QR factorization with pivoting of A, */
/* > whose estimated condition number < 1/RCOND. */
/* > \endverbatim */
/* > */
/* > \param[out] RANK */
/* > \verbatim */
/* > RANK is INTEGER */
/* > The effective rank of A, i.e., the order of the submatrix */
/* > R11. This is the same as the order of the submatrix T11 */
/* > in the complete orthogonal factorization of A. */
/* > \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. */
/* > The unblocked strategy requires that: */
/* > LWORK >= MN + MAX( 2*MN, N+1, MN+NRHS ) */
/* > where MN = f2cmin(M,N). */
/* > The block algorithm requires that: */
/* > LWORK >= MN + MAX( 2*MN, NB*(N+1), MN+MN*NB, MN+NB*NRHS ) */
/* > where NB is an upper bound on the blocksize returned */
/* > by ILAENV for the routines CGEQP3, CTZRZF, CTZRQF, CUNMQR, */
/* > and CUNMRZ. */
/* > */
/* > If LWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates the optimal size of the WORK array, returns */
/* > this value as the first entry of the WORK array, and no error */
/* > message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* > RWORK is REAL array, dimension (2*N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
/* > \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: */
/* ================== */
/* > */
/* > A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA \n */
/* > E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n */
/* > G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n */
/* > */
/* ===================================================================== */
/* Subroutine */voidcgelsy_(integer*m, integer*n, integer*nrhs, complex*
a, integer*lda, complex*b, integer*ldb, integer*jpvt, real*rcond,
integer*rank, complex*work, integer*lwork, real*rwork, integer*
info)
{
/* System generated locals */
integera_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
realr__1, r__2;
complexq__1;

/* Local variables */
realanrm, bnrm, smin, smax;
integeri__, j, iascl, ibscl;
extern/* Subroutine */voidccopy_(integer*, complex*, integer*, 
complex*, integer*);
integerismin, ismax;
complexc1, c2;
extern/* Subroutine */voidctrsm_(char*, char*, char*, char*, 
integer*, integer*, complex*, complex*, integer*, complex*, 
integer*), claic1_(integer*, 
integer*, complex*, real*, complex*, complex*, real*, 
complex*, complex*);
realwsize;
complexs1, s2;
extern/* Subroutine */voidcgeqp3_(integer*, integer*, complex*, 
integer*, integer*, complex*, complex*, integer*, real*, 
integer*);
integernb;
extern/* Subroutine */voidslabad_(real*, real*);
externrealclange_(char*, integer*, integer*, complex*, integer*, 
real*);
integermn;
extern/* Subroutine */voidclascl_(char*, integer*, integer*, real*, 
real*, integer*, integer*, complex*, integer*, integer*);
externrealslamch_(char*);
extern/* Subroutine */voidclaset_(char*, integer*, integer*, complex
*, complex*, complex*, integer*);
externintxerbla_(char*, integer*, ftnlen);
externintegerilaenv_(integer*, char*, char*, integer*, integer*, 
integer*, integer*, ftnlen, ftnlen);
realbignum;
integernb1, nb2, nb3, nb4;
extern/* Subroutine */voidcunmqr_(char*, char*, integer*, integer*, 
integer*, complex*, integer*, complex*, complex*, integer*, 
complex*, integer*, integer*);
realsminpr, smaxpr, smlnum;
extern/* Subroutine */voidcunmrz_(char*, char*, integer*, integer*, 
integer*, integer*, complex*, integer*, complex*, complex*, 
integer*, complex*, integer*, integer*);
integerlwkopt;
logicallquery;
extern/* Subroutine */voidctzrzf_(integer*, integer*, complex*, 
integer*, complex*, complex*, integer*, integer*);


/* -- 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 */


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


/* 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;
--jpvt;
--work;
--rwork;

/* Function Body */
mn=f2cmin(*m,*n);
ismin=mn+1;
ismax= (mn << 1) +1;

/* Test the input arguments. */

*info=0;
nb1=ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
nb2=ilaenv_(&c__1, "CGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
nb3=ilaenv_(&c__1, "CUNMQR", " ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)
1);
nb4=ilaenv_(&c__1, "CUNMRQ", " ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)
1);
/* Computing MAX */
i__1=f2cmax(nb1,nb2), i__1=f2cmax(i__1,nb3);
nb=f2cmax(i__1,nb4);
/* Computing MAX */
i__1=1, i__2=mn+ (*n << 1) +nb* (*n+1), i__1=f2cmax(i__1,i__2), 
i__2= (mn << 1) +nb**nrhs;
lwkopt=f2cmax(i__1,i__2);
q__1.r= (real) lwkopt, q__1.i=0.f;
work[1].r=q__1.r, work[1].i=q__1.i;
lquery=*lwork==-1;
if (*m<0) {
*info=-1;
 } elseif (*n<0) {
*info=-2;
 } elseif (*nrhs<0) {
*info=-3;
 } elseif (*lda<f2cmax(1,*m)) {
*info=-5;
 } else/* if(complicated condition) */ {
/* Computing MAX */
i__1=f2cmax(1,*m);
if (*ldb<f2cmax(i__1,*n)) {
*info=-7;
 } else/* if(complicated condition) */ {
/* Computing MAX */
i__1=mn << 1, i__2=*n+1, i__1=f2cmax(i__1,i__2), i__2=mn+
*nrhs;
if (*lwork<mn+f2cmax(i__1,i__2) && ! lquery) {
*info=-12;
 }
 }
 }

if (*info!=0) {
i__1=-(*info);
xerbla_("CGELSY", &i__1, (ftnlen)6);
return;
 } elseif (lquery) {
return;
 }

/* Quick return if possible */

/* Computing MIN */
i__1=f2cmin(*m,*n);
if (f2cmin(i__1,*nrhs) ==0) {
*rank=0;
return;
 }

/* Get machine parameters */

smlnum=slamch_("S") / slamch_("P");
bignum=1.f / smlnum;
slabad_(&smlnum, &bignum);

/* Scale A, B if f2cmax entries outside range [SMLNUM,BIGNUM] */

anrm=clange_("M", m, n, &a[a_offset], lda, &rwork[1]);
iascl=0;
if (anrm>0.f&&anrm<smlnum) {

/* Scale matrix norm up to SMLNUM */

clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, 
info);
iascl=1;
 } elseif (anrm>bignum) {

/* Scale matrix norm down to BIGNUM */

clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
info);
iascl=2;
 } elseif (anrm==0.f) {

/* Matrix all zero. Return zero solution. */

i__1=f2cmax(*m,*n);
claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
*rank=0;
 goto L70;
 }

bnrm=clange_("M", m, nrhs, &b[b_offset], ldb, &rwork[1]);
ibscl=0;
if (bnrm>0.f&&bnrm<smlnum) {

/* Scale matrix norm up to SMLNUM */

clascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
info);
ibscl=1;
 } elseif (bnrm>bignum) {

/* Scale matrix norm down to BIGNUM */

clascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
info);
ibscl=2;
 }

/* Compute QR factorization with column pivoting of A: */
/* A * P = Q * R */

i__1=*lwork-mn;
cgeqp3_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn+1], &i__1,
&rwork[1], info);
i__1=mn+1;
wsize=mn+work[i__1].r;

/* complex workspace: MN+NB*(N+1). real workspace 2*N. */
/* Details of Householder rotations stored in WORK(1:MN). */

/* Determine RANK using incremental condition estimation */

i__1=ismin;
work[i__1].r=1.f, work[i__1].i=0.f;
i__1=ismax;
work[i__1].r=1.f, work[i__1].i=0.f;
smax=c_abs(&a[a_dim1+1]);
smin=smax;
if (c_abs(&a[a_dim1+1]) ==0.f) {
*rank=0;
i__1=f2cmax(*m,*n);
claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
 goto L70;
 } else {
*rank=1;
 }

L10:
if (*rank<mn) {
i__=*rank+1;
claic1_(&c__2, rank, &work[ismin], &smin, &a[i__*a_dim1+1], &a[
i__+i__*a_dim1], &sminpr, &s1, &c1);
claic1_(&c__1, rank, &work[ismax], &smax, &a[i__*a_dim1+1], &a[
i__+i__*a_dim1], &smaxpr, &s2, &c2);

if (smaxpr**rcond <= sminpr) {
i__1=*rank;
for (i__=1; i__ <= i__1; ++i__) {
i__2=ismin+i__-1;
i__3=ismin+i__-1;
q__1.r=s1.r*work[i__3].r-s1.i*work[i__3].i, q__1.i=
s1.r*work[i__3].i+s1.i*work[i__3].r;
work[i__2].r=q__1.r, work[i__2].i=q__1.i;
i__2=ismax+i__-1;
i__3=ismax+i__-1;
q__1.r=s2.r*work[i__3].r-s2.i*work[i__3].i, q__1.i=
s2.r*work[i__3].i+s2.i*work[i__3].r;
work[i__2].r=q__1.r, work[i__2].i=q__1.i;
/* L20: */
 }
i__1=ismin+*rank;
work[i__1].r=c1.r, work[i__1].i=c1.i;
i__1=ismax+*rank;
work[i__1].r=c2.r, work[i__1].i=c2.i;
smin=sminpr;
smax=smaxpr;
++(*rank);
 goto L10;
 }
 }

/* complex workspace: 3*MN. */

/* Logically partition R = [ R11 R12 ] */
/* [ 0 R22 ] */
/* where R11 = R(1:RANK,1:RANK) */

/* [R11,R12] = [ T11, 0 ] * Y */

if (*rank<*n) {
i__1=*lwork- (mn << 1);
ctzrzf_(rank, n, &a[a_offset], lda, &work[mn+1], &work[(mn << 1) +
1], &i__1, info);
 }

/* complex workspace: 2*MN. */