cgejsv.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_n1=-1;
staticintegerc__1=1;
staticintegerc__0=0;
staticrealc_b141=1.f;
staticlogicalc_false=FALSE_;

/* > \brief \b CGEJSV */

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

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

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

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

/* SUBROUTINE CGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP, */
/* M, N, A, LDA, SVA, U, LDU, V, LDV, */
/* CWORK, LWORK, RWORK, LRWORK, IWORK, INFO ) */

/* IMPLICIT NONE */
/* INTEGER INFO, LDA, LDU, LDV, LWORK, M, N */
/* COMPLEX A( LDA, * ), U( LDU, * ), V( LDV, * ), CWORK( LWORK ) */
/* REAL SVA( N ), RWORK( LRWORK ) */
/* INTEGER IWORK( * ) */
/* CHARACTER*1 JOBA, JOBP, JOBR, JOBT, JOBU, JOBV */


/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CGEJSV computes the singular value decomposition (SVD) of a complex M-by-N */
/* > matrix [A], where M >= N. The SVD of [A] is written as */
/* > */
/* > [A] = [U] * [SIGMA] * [V]^*, */
/* > */
/* > where [SIGMA] is an N-by-N (M-by-N) matrix which is zero except for its N */
/* > diagonal elements, [U] is an M-by-N (or M-by-M) unitary matrix, and */
/* > [V] is an N-by-N unitary matrix. The diagonal elements of [SIGMA] are */
/* > the singular values of [A]. The columns of [U] and [V] are the left and */
/* > the right singular vectors of [A], respectively. The matrices [U] and [V] */
/* > are computed and stored in the arrays U and V, respectively. The diagonal */
/* > of [SIGMA] is computed and stored in the array SVA. */
/* > \endverbatim */
/* > */
/* > Arguments: */
/* > ========== */
/* > */
/* > \param[in] JOBA */
/* > \verbatim */
/* > JOBA is CHARACTER*1 */
/* > Specifies the level of accuracy: */
/* > = 'C': This option works well (high relative accuracy) if A = B * D, */
/* > with well-conditioned B and arbitrary diagonal matrix D. */
/* > The accuracy cannot be spoiled by COLUMN scaling. The */
/* > accuracy of the computed output depends on the condition of */
/* > B, and the procedure aims at the best theoretical accuracy. */
/* > The relative error max_{i=1:N}|d sigma_i| / sigma_i is */
/* > bounded by f(M,N)*epsilon* cond(B), independent of D. */
/* > The input matrix is preprocessed with the QRF with column */
/* > pivoting. This initial preprocessing and preconditioning by */
/* > a rank revealing QR factorization is common for all values of */
/* > JOBA. Additional actions are specified as follows: */
/* > = 'E': Computation as with 'C' with an additional estimate of the */
/* > condition number of B. It provides a realistic error bound. */
/* > = 'F': If A = D1 * C * D2 with ill-conditioned diagonal scalings */
/* > D1, D2, and well-conditioned matrix C, this option gives */
/* > higher accuracy than the 'C' option. If the structure of the */
/* > input matrix is not known, and relative accuracy is */
/* > desirable, then this option is advisable. The input matrix A */
/* > is preprocessed with QR factorization with FULL (row and */
/* > column) pivoting. */
/* > = 'G': Computation as with 'F' with an additional estimate of the */
/* > condition number of B, where A=B*D. If A has heavily weighted */
/* > rows, then using this condition number gives too pessimistic */
/* > error bound. */
/* > = 'A': Small singular values are not well determined by the data */
/* > and are considered as noisy; the matrix is treated as */
/* > numerically rank deficient. The error in the computed */
/* > singular values is bounded by f(m,n)*epsilon*||A||. */
/* > The computed SVD A = U * S * V^* restores A up to */
/* > f(m,n)*epsilon*||A||. */
/* > This gives the procedure the licence to discard (set to zero) */
/* > all singular values below N*epsilon*||A||. */
/* > = 'R': Similar as in 'A'. Rank revealing property of the initial */
/* > QR factorization is used do reveal (using triangular factor) */
/* > a gap sigma_{r+1} < epsilon * sigma_r in which case the */
/* > numerical RANK is declared to be r. The SVD is computed with */
/* > absolute error bounds, but more accurately than with 'A'. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBU */
/* > \verbatim */
/* > JOBU is CHARACTER*1 */
/* > Specifies whether to compute the columns of U: */
/* > = 'U': N columns of U are returned in the array U. */
/* > = 'F': full set of M left sing. vectors is returned in the array U. */
/* > = 'W': U may be used as workspace of length M*N. See the description */
/* > of U. */
/* > = 'N': U is not computed. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBV */
/* > \verbatim */
/* > JOBV is CHARACTER*1 */
/* > Specifies whether to compute the matrix V: */
/* > = 'V': N columns of V are returned in the array V; Jacobi rotations */
/* > are not explicitly accumulated. */
/* > = 'J': N columns of V are returned in the array V, but they are */
/* > computed as the product of Jacobi rotations, if JOBT = 'N'. */
/* > = 'W': V may be used as workspace of length N*N. See the description */
/* > of V. */
/* > = 'N': V is not computed. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBR */
/* > \verbatim */
/* > JOBR is CHARACTER*1 */
/* > Specifies the RANGE for the singular values. Issues the licence to */
/* > set to zero small positive singular values if they are outside */
/* > specified range. If A .NE. 0 is scaled so that the largest singular */
/* > value of c*A is around SQRT(BIG), BIG=SLAMCH('O'), then JOBR issues */
/* > the licence to kill columns of A whose norm in c*A is less than */
/* > SQRT(SFMIN) (for JOBR = 'R'), or less than SMALL=SFMIN/EPSLN, */
/* > where SFMIN=SLAMCH('S'), EPSLN=SLAMCH('E'). */
/* > = 'N': Do not kill small columns of c*A. This option assumes that */
/* > BLAS and QR factorizations and triangular solvers are */
/* > implemented to work in that range. If the condition of A */
/* > is greater than BIG, use CGESVJ. */
/* > = 'R': RESTRICTED range for sigma(c*A) is [SQRT(SFMIN), SQRT(BIG)] */
/* > (roughly, as described above). This option is recommended. */
/* > =========================== */
/* > For computing the singular values in the FULL range [SFMIN,BIG] */
/* > use CGESVJ. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBT */
/* > \verbatim */
/* > JOBT is CHARACTER*1 */
/* > If the matrix is square then the procedure may determine to use */
/* > transposed A if A^* seems to be better with respect to convergence. */
/* > If the matrix is not square, JOBT is ignored. */
/* > The decision is based on two values of entropy over the adjoint */
/* > orbit of A^* * A. See the descriptions of WORK(6) and WORK(7). */
/* > = 'T': transpose if entropy test indicates possibly faster */
/* > convergence of Jacobi process if A^* is taken as input. If A is */
/* > replaced with A^*, then the row pivoting is included automatically. */
/* > = 'N': do not speculate. */
/* > The option 'T' can be used to compute only the singular values, or */
/* > the full SVD (U, SIGMA and V). For only one set of singular vectors */
/* > (U or V), the caller should provide both U and V, as one of the */
/* > matrices is used as workspace if the matrix A is transposed. */
/* > The implementer can easily remove this constraint and make the */
/* > code more complicated. See the descriptions of U and V. */
/* > In general, this option is considered experimental, and 'N'; should */
/* > be preferred. This is subject to changes in the future. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBP */
/* > \verbatim */
/* > JOBP is CHARACTER*1 */
/* > Issues the licence to introduce structured perturbations to drown */
/* > denormalized numbers. This licence should be active if the */
/* > denormals are poorly implemented, causing slow computation, */
/* > especially in cases of fast convergence (!). For details see [1,2]. */
/* > For the sake of simplicity, this perturbations are included only */
/* > when the full SVD or only the singular values are requested. The */
/* > implementer/user can easily add the perturbation for the cases of */
/* > computing one set of singular vectors. */
/* > = 'P': introduce perturbation */
/* > = 'N': do not perturb */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The number of rows of the input matrix A. M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of columns of the input matrix A. M >= N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is COMPLEX array, dimension (LDA,N) */
/* > On entry, the M-by-N matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[out] SVA */
/* > \verbatim */
/* > SVA is REAL array, dimension (N) */
/* > On exit, */
/* > - For WORK(1)/WORK(2) = ONE: The singular values of A. During the */
/* > computation SVA contains Euclidean column norms of the */
/* > iterated matrices in the array A. */
/* > - For WORK(1) .NE. WORK(2): The singular values of A are */
/* > (WORK(1)/WORK(2)) * SVA(1:N). This factored form is used if */
/* > sigma_max(A) overflows or if small singular values have been */
/* > saved from underflow by scaling the input matrix A. */
/* > - If JOBR='R' then some of the singular values may be returned */
/* > as exact zeros obtained by "set to zero" because they are */
/* > below the numerical rank threshold or are denormalized numbers. */
/* > \endverbatim */
/* > */
/* > \param[out] U */
/* > \verbatim */
/* > U is COMPLEX array, dimension ( LDU, N ) or ( LDU, M ) */
/* > If JOBU = 'U', then U contains on exit the M-by-N matrix of */
/* > the left singular vectors. */
/* > If JOBU = 'F', then U contains on exit the M-by-M matrix of */
/* > the left singular vectors, including an ONB */
/* > of the orthogonal complement of the Range(A). */
/* > If JOBU = 'W' .AND. (JOBV = 'V' .AND. JOBT = 'T' .AND. M = N), */
/* > then U is used as workspace if the procedure */
/* > replaces A with A^*. In that case, [V] is computed */
/* > in U as left singular vectors of A^* and then */
/* > copied back to the V array. This 'W' option is just */
/* > a reminder to the caller that in this case U is */
/* > reserved as workspace of length N*N. */
/* > If JOBU = 'N' U is not referenced, unless JOBT='T'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* > LDU is INTEGER */
/* > The leading dimension of the array U, LDU >= 1. */
/* > IF JOBU = 'U' or 'F' or 'W', then LDU >= M. */
/* > \endverbatim */
/* > */
/* > \param[out] V */
/* > \verbatim */
/* > V is COMPLEX array, dimension ( LDV, N ) */
/* > If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of */
/* > the right singular vectors; */
/* > If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N), */
/* > then V is used as workspace if the pprocedure */
/* > replaces A with A^*. In that case, [U] is computed */
/* > in V as right singular vectors of A^* and then */
/* > copied back to the U array. This 'W' option is just */
/* > a reminder to the caller that in this case V is */
/* > reserved as workspace of length N*N. */
/* > If JOBV = 'N' V is not referenced, unless JOBT='T'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDV */
/* > \verbatim */
/* > LDV is INTEGER */
/* > The leading dimension of the array V, LDV >= 1. */
/* > If JOBV = 'V' or 'J' or 'W', then LDV >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] CWORK */
/* > \verbatim */
/* > CWORK is COMPLEX array, dimension (MAX(2,LWORK)) */
/* > If the call to CGEJSV is a workspace query (indicated by LWORK=-1 or */
/* > LRWORK=-1), then on exit CWORK(1) contains the required length of */
/* > CWORK for the job parameters used in the call. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > Length of CWORK to confirm proper allocation of workspace. */
/* > LWORK depends on the job: */
/* > */
/* > 1. If only SIGMA is needed ( JOBU = 'N', JOBV = 'N' ) and */
/* > 1.1 .. no scaled condition estimate required (JOBA.NE.'E'.AND.JOBA.NE.'G'): */
/* > LWORK >= 2*N+1. This is the minimal requirement. */
/* > ->> For optimal performance (blocked code) the optimal value */
/* > is LWORK >= N + (N+1)*NB. Here NB is the optimal */
/* > block size for CGEQP3 and CGEQRF. */
/* > In general, optimal LWORK is computed as */
/* > LWORK >= f2cmax(N+LWORK(CGEQP3),N+LWORK(CGEQRF), LWORK(CGESVJ)). */
/* > 1.2. .. an estimate of the scaled condition number of A is */
/* > required (JOBA='E', or 'G'). In this case, LWORK the minimal */
/* > requirement is LWORK >= N*N + 2*N. */
/* > ->> For optimal performance (blocked code) the optimal value */
/* > is LWORK >= f2cmax(N+(N+1)*NB, N*N+2*N)=N**2+2*N. */
/* > In general, the optimal length LWORK is computed as */
/* > LWORK >= f2cmax(N+LWORK(CGEQP3),N+LWORK(CGEQRF), LWORK(CGESVJ), */
/* > N*N+LWORK(CPOCON)). */
/* > 2. If SIGMA and the right singular vectors are needed (JOBV = 'V'), */
/* > (JOBU = 'N') */
/* > 2.1 .. no scaled condition estimate requested (JOBE = 'N'): */
/* > -> the minimal requirement is LWORK >= 3*N. */
/* > -> For optimal performance, */
/* > LWORK >= f2cmax(N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB, */
/* > where NB is the optimal block size for CGEQP3, CGEQRF, CGELQ, */
/* > CUNMLQ. In general, the optimal length LWORK is computed as */
/* > LWORK >= f2cmax(N+LWORK(CGEQP3), N+LWORK(CGESVJ), */
/* > N+LWORK(CGELQF), 2*N+LWORK(CGEQRF), N+LWORK(CUNMLQ)). */
/* > 2.2 .. an estimate of the scaled condition number of A is */
/* > required (JOBA='E', or 'G'). */
/* > -> the minimal requirement is LWORK >= 3*N. */
/* > -> For optimal performance, */
/* > LWORK >= f2cmax(N+(N+1)*NB, 2*N,2*N+N*NB)=2*N+N*NB, */
/* > where NB is the optimal block size for CGEQP3, CGEQRF, CGELQ, */
/* > CUNMLQ. In general, the optimal length LWORK is computed as */
/* > LWORK >= f2cmax(N+LWORK(CGEQP3), LWORK(CPOCON), N+LWORK(CGESVJ), */
/* > N+LWORK(CGELQF), 2*N+LWORK(CGEQRF), N+LWORK(CUNMLQ)). */
/* > 3. If SIGMA and the left singular vectors are needed */
/* > 3.1 .. no scaled condition estimate requested (JOBE = 'N'): */
/* > -> the minimal requirement is LWORK >= 3*N. */
/* > -> For optimal performance: */
/* > if JOBU = 'U' :: LWORK >= f2cmax(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB, */
/* > where NB is the optimal block size for CGEQP3, CGEQRF, CUNMQR. */
/* > In general, the optimal length LWORK is computed as */
/* > LWORK >= f2cmax(N+LWORK(CGEQP3), 2*N+LWORK(CGEQRF), N+LWORK(CUNMQR)). */
/* > 3.2 .. an estimate of the scaled condition number of A is */
/* > required (JOBA='E', or 'G'). */
/* > -> the minimal requirement is LWORK >= 3*N. */
/* > -> For optimal performance: */
/* > if JOBU = 'U' :: LWORK >= f2cmax(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB, */
/* > where NB is the optimal block size for CGEQP3, CGEQRF, CUNMQR. */
/* > In general, the optimal length LWORK is computed as */
/* > LWORK >= f2cmax(N+LWORK(CGEQP3),N+LWORK(CPOCON), */
/* > 2*N+LWORK(CGEQRF), N+LWORK(CUNMQR)). */
/* > */
/* > 4. If the full SVD is needed: (JOBU = 'U' or JOBU = 'F') and */
/* > 4.1. if JOBV = 'V' */
/* > the minimal requirement is LWORK >= 5*N+2*N*N. */
/* > 4.2. if JOBV = 'J' the minimal requirement is */
/* > LWORK >= 4*N+N*N. */
/* > In both cases, the allocated CWORK can accommodate blocked runs */
/* > of CGEQP3, CGEQRF, CGELQF, CUNMQR, CUNMLQ. */
/* > */
/* > If the call to CGEJSV is a workspace query (indicated by LWORK=-1 or */
/* > LRWORK=-1), then on exit CWORK(1) contains the optimal and CWORK(2) contains the */
/* > minimal length of CWORK for the job parameters used in the call. */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* > RWORK is REAL array, dimension (MAX(7,LWORK)) */
/* > On exit, */
/* > RWORK(1) = Determines the scaling factor SCALE = RWORK(2) / RWORK(1) */
/* > such that SCALE*SVA(1:N) are the computed singular values */
/* > of A. (See the description of SVA().) */
/* > RWORK(2) = See the description of RWORK(1). */
/* > RWORK(3) = SCONDA is an estimate for the condition number of */
/* > column equilibrated A. (If JOBA = 'E' or 'G') */
/* > SCONDA is an estimate of SQRT(||(R^* * R)^(-1)||_1). */
/* > It is computed using SPOCON. It holds */
/* > N^(-1/4) * SCONDA <= ||R^(-1)||_2 <= N^(1/4) * SCONDA */
/* > where R is the triangular factor from the QRF of A. */
/* > However, if R is truncated and the numerical rank is */
/* > determined to be strictly smaller than N, SCONDA is */
/* > returned as -1, thus indicating that the smallest */
/* > singular values might be lost. */
/* > */
/* > If full SVD is needed, the following two condition numbers are */
/* > useful for the analysis of the algorithm. They are provied for */
/* > a developer/implementer who is familiar with the details of */
/* > the method. */
/* > */
/* > RWORK(4) = an estimate of the scaled condition number of the */
/* > triangular factor in the first QR factorization. */
/* > RWORK(5) = an estimate of the scaled condition number of the */
/* > triangular factor in the second QR factorization. */
/* > The following two parameters are computed if JOBT = 'T'. */
/* > They are provided for a developer/implementer who is familiar */
/* > with the details of the method. */
/* > RWORK(6) = the entropy of A^* * A :: this is the Shannon entropy */
/* > of diag(A^* * A) / Trace(A^* * A) taken as point in the */
/* > probability simplex. */
/* > RWORK(7) = the entropy of A * A^*. (See the description of RWORK(6).) */
/* > If the call to CGEJSV is a workspace query (indicated by LWORK=-1 or */
/* > LRWORK=-1), then on exit RWORK(1) contains the required length of */
/* > RWORK for the job parameters used in the call. */
/* > \endverbatim */
/* > */
/* > \param[in] LRWORK */
/* > \verbatim */
/* > LRWORK is INTEGER */
/* > Length of RWORK to confirm proper allocation of workspace. */
/* > LRWORK depends on the job: */
/* > */
/* > 1. If only the singular values are requested i.e. if */
/* > LSAME(JOBU,'N') .AND. LSAME(JOBV,'N') */
/* > then: */
/* > 1.1. If LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G'), */
/* > then: LRWORK = f2cmax( 7, 2 * M ). */
/* > 1.2. Otherwise, LRWORK = f2cmax( 7, N ). */
/* > 2. If singular values with the right singular vectors are requested */
/* > i.e. if */
/* > (LSAME(JOBV,'V').OR.LSAME(JOBV,'J')) .AND. */
/* > .NOT.(LSAME(JOBU,'U').OR.LSAME(JOBU,'F')) */
/* > then: */
/* > 2.1. If LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G'), */
/* > then LRWORK = f2cmax( 7, 2 * M ). */
/* > 2.2. Otherwise, LRWORK = f2cmax( 7, N ). */
/* > 3. If singular values with the left singular vectors are requested, i.e. if */
/* > (LSAME(JOBU,'U').OR.LSAME(JOBU,'F')) .AND. */
/* > .NOT.(LSAME(JOBV,'V').OR.LSAME(JOBV,'J')) */
/* > then: */
/* > 3.1. If LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G'), */
/* > then LRWORK = f2cmax( 7, 2 * M ). */
/* > 3.2. Otherwise, LRWORK = f2cmax( 7, N ). */
/* > 4. If singular values with both the left and the right singular vectors */
/* > are requested, i.e. if */
/* > (LSAME(JOBU,'U').OR.LSAME(JOBU,'F')) .AND. */
/* > (LSAME(JOBV,'V').OR.LSAME(JOBV,'J')) */
/* > then: */
/* > 4.1. If LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G'), */
/* > then LRWORK = f2cmax( 7, 2 * M ). */
/* > 4.2. Otherwise, LRWORK = f2cmax( 7, N ). */
/* > */
/* > If, on entry, LRWORK = -1 or LWORK=-1, a workspace query is assumed and */
/* > the length of RWORK is returned in RWORK(1). */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, of dimension at least 4, that further depends */
/* > on the job: */
/* > */
/* > 1. If only the singular values are requested then: */
/* > If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') ) */
/* > then the length of IWORK is N+M; otherwise the length of IWORK is N. */
/* > 2. If the singular values and the right singular vectors are requested then: */
/* > If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') ) */
/* > then the length of IWORK is N+M; otherwise the length of IWORK is N. */
/* > 3. If the singular values and the left singular vectors are requested then: */
/* > If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') ) */
/* > then the length of IWORK is N+M; otherwise the length of IWORK is N. */
/* > 4. If the singular values with both the left and the right singular vectors */
/* > are requested, then: */
/* > 4.1. If LSAME(JOBV,'J') the length of IWORK is determined as follows: */
/* > If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') ) */
/* > then the length of IWORK is N+M; otherwise the length of IWORK is N. */
/* > 4.2. If LSAME(JOBV,'V') the length of IWORK is determined as follows: */
/* > If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') ) */
/* > then the length of IWORK is 2*N+M; otherwise the length of IWORK is 2*N. */
/* > */
/* > On exit, */
/* > IWORK(1) = the numerical rank determined after the initial */
/* > QR factorization with pivoting. See the descriptions */
/* > of JOBA and JOBR. */
/* > IWORK(2) = the number of the computed nonzero singular values */
/* > IWORK(3) = if nonzero, a warning message: */
/* > If IWORK(3) = 1 then some of the column norms of A */
/* > were denormalized floats. The requested high accuracy */
/* > is not warranted by the data. */
/* > IWORK(4) = 1 or -1. If IWORK(4) = 1, then the procedure used A^* to */
/* > do the job as specified by the JOB parameters. */
/* > If the call to CGEJSV is a workspace query (indicated by LWORK = -1 and */
/* > LRWORK = -1), then on exit IWORK(1) contains the required length of */
/* > IWORK for the job parameters used in the call. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > < 0: if INFO = -i, then the i-th argument had an illegal value. */
/* > = 0: successful exit; */
/* > > 0: CGEJSV did not converge in the maximal allowed number */
/* > of sweeps. The computed values may be inaccurate. */
/* > \endverbatim */