lapack-netlib/SRC/cgsvj0.c

   1 #include <math.h>
   2 #include <stdlib.h>
   3 #include <string.h>
   4 #include <stdio.h>
   5 #include <complex.h>
   6 #ifdef complex
   7 #undef complex
   8 #endif
   9 #ifdef I
  10 #undef I
  11 #endif
  12
  13 #if defined(_WIN64)
  14 typedef long long BLASLONG;
  15 typedef unsigned long long BLASULONG;
  16 #else
  17 typedef long BLASLONG;
  18 typedef unsigned long BLASULONG;
  19 #endif
  20
  21 #ifdef LAPACK_ILP64
  22 typedef BLASLONG blasint;
  23 #if defined(_WIN64)
  24 #define blasabs(x) llabs(x)
  25 #else
  26 #define blasabs(x) labs(x)
  27 #endif
  28 #else
  29 typedef int blasint;
  30 #define blasabs(x) abs(x)
  31 #endif
  32
  33 typedef blasint integer;
  34
  35 typedef unsigned int uinteger;
  36 typedef char *address;
  37 typedef short int shortint;
  38 typedef float real;
  39 typedef double doublereal;
  40 typedef struct { real r, i; } complex;
  41 typedef struct { doublereal r, i; } doublecomplex;
  42 #ifdef _MSC_VER
  43 static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
  44 static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
  45 static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
  46 static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
  47 #else
  48 static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  49 static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  50 static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  51 static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  52 #endif
  53 #define pCf(z) (*_pCf(z))
  54 #define pCd(z) (*_pCd(z))
  55 typedef int logical;
  56 typedef short int shortlogical;
  57 typedef char logical1;
  58 typedef char integer1;
  59
  60 #define TRUE_ (1)
  61 #define FALSE_ (0)
  62
  63 /* Extern is for use with -E */
  64 #ifndef Extern
  65 #define Extern extern
  66 #endif
  67
  68 /* I/O stuff */
  69
  70 typedef int flag;
  71 typedef int ftnlen;
  72 typedef int ftnint;
  73
  74 /*external read, write*/
  75 typedef struct
  76 {       flag cierr;
  77         ftnint ciunit;
  78         flag ciend;
  79         char *cifmt;
  80         ftnint cirec;
  81 } cilist;
  82
  83 /*internal read, write*/
  84 typedef struct
  85 {       flag icierr;
  86         char *iciunit;
  87         flag iciend;
  88         char *icifmt;
  89         ftnint icirlen;
  90         ftnint icirnum;
  91 } icilist;
  92
  93 /*open*/
  94 typedef struct
  95 {       flag oerr;
  96         ftnint ounit;
  97         char *ofnm;
  98         ftnlen ofnmlen;
  99         char *osta;
 100         char *oacc;
 101         char *ofm;
 102         ftnint orl;
 103         char *oblnk;
 104 } olist;
 105
 106 /*close*/
 107 typedef struct
 108 {       flag cerr;
 109         ftnint cunit;
 110         char *csta;
 111 } cllist;
 112
 113 /*rewind, backspace, endfile*/
 114 typedef struct
 115 {       flag aerr;
 116         ftnint aunit;
 117 } alist;
 118
 119 /* inquire */
 120 typedef struct
 121 {       flag inerr;
 122         ftnint inunit;
 123         char *infile;
 124         ftnlen infilen;
 125         ftnint  *inex;  /*parameters in standard's order*/
 126         ftnint  *inopen;
 127         ftnint  *innum;
 128         ftnint  *innamed;
 129         char    *inname;
 130         ftnlen  innamlen;
 131         char    *inacc;
 132         ftnlen  inacclen;
 133         char    *inseq;
 134         ftnlen  inseqlen;
 135         char    *indir;
 136         ftnlen  indirlen;
 137         char    *infmt;
 138         ftnlen  infmtlen;
 139         char    *inform;
 140         ftnint  informlen;
 141         char    *inunf;
 142         ftnlen  inunflen;
 143         ftnint  *inrecl;
 144         ftnint  *innrec;
 145         char    *inblank;
 146         ftnlen  inblanklen;
 147 } inlist;
 148
 149 #define VOID void
 150
 151 union Multitype {       /* for multiple entry points */
 152         integer1 g;
 153         shortint h;
 154         integer i;
 155         /* longint j; */
 156         real r;
 157         doublereal d;
 158         complex c;
 159         doublecomplex z;
 160         };
 161
 162 typedef union Multitype Multitype;
 163
 164 struct Vardesc {        /* for Namelist */
 165         char *name;
 166         char *addr;
 167         ftnlen *dims;
 168         int  type;
 169         };
 170 typedef struct Vardesc Vardesc;
 171
 172 struct Namelist {
 173         char *name;
 174         Vardesc **vars;
 175         int nvars;
 176         };
 177 typedef struct Namelist Namelist;
 178
 179 #define abs(x) ((x) >= 0 ? (x) : -(x))
 180 #define dabs(x) (fabs(x))
 181 #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
 182 #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
 183 #define dmin(a,b) (f2cmin(a,b))
 184 #define dmax(a,b) (f2cmax(a,b))
 185 #define bit_test(a,b)   ((a) >> (b) & 1)
 186 #define bit_clear(a,b)  ((a) & ~((uinteger)1 << (b)))
 187 #define bit_set(a,b)    ((a) |  ((uinteger)1 << (b)))
 188
 189 #define abort_() { sig_die("Fortran abort routine called", 1); }
 190 #define c_abs(z) (cabsf(Cf(z)))
 191 #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
 192 #ifdef _MSC_VER
 193 #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]);}
 194 #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]);}
 195 #else
 196 #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
 197 #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
 198 #endif
 199 #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
 200 #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
 201 #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
 202 //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
 203 #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
 204 #define d_abs(x) (fabs(*(x)))
 205 #define d_acos(x) (acos(*(x)))
 206 #define d_asin(x) (asin(*(x)))
 207 #define d_atan(x) (atan(*(x)))
 208 #define d_atn2(x, y) (atan2(*(x),*(y)))
 209 #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
 210 #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
 211 #define d_cos(x) (cos(*(x)))
 212 #define d_cosh(x) (cosh(*(x)))
 213 #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
 214 #define d_exp(x) (exp(*(x)))
 215 #define d_imag(z) (cimag(Cd(z)))
 216 #define r_imag(z) (cimagf(Cf(z)))
 217 #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
 218 #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
 219 #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
 220 #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
 221 #define d_log(x) (log(*(x)))
 222 #define d_mod(x, y) (fmod(*(x), *(y)))
 223 #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
 224 #define d_nint(x) u_nint(*(x))
 225 #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
 226 #define d_sign(a,b) u_sign(*(a),*(b))
 227 #define r_sign(a,b) u_sign(*(a),*(b))
 228 #define d_sin(x) (sin(*(x)))
 229 #define d_sinh(x) (sinh(*(x)))
 230 #define d_sqrt(x) (sqrt(*(x)))
 231 #define d_tan(x) (tan(*(x)))
 232 #define d_tanh(x) (tanh(*(x)))
 233 #define i_abs(x) abs(*(x))
 234 #define i_dnnt(x) ((integer)u_nint(*(x)))
 235 #define i_len(s, n) (n)
 236 #define i_nint(x) ((integer)u_nint(*(x)))
 237 #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
 238 #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
 239 #define pow_si(B,E) spow_ui(*(B),*(E))
 240 #define pow_ri(B,E) spow_ui(*(B),*(E))
 241 #define pow_di(B,E) dpow_ui(*(B),*(E))
 242 #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
 243 #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
 244 #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
 245 #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++ = ' '; }
 246 #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
 247 #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]; }
 248 #define sig_die(s, kill) { exit(1); }
 249 #define s_stop(s, n) {exit(0);}
 250 static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
 251 #define z_abs(z) (cabs(Cd(z)))
 252 #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
 253 #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
 254 #define myexit_() break;
 255 #define mycycle() continue;
 256 #define myceiling(w) {ceil(w)}
 257 #define myhuge(w) {HUGE_VAL}
 258 //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
 259 #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
 260
 261 /* procedure parameter types for -A and -C++ */
 262
 263 #define F2C_proc_par_types 1
 264 #ifdef __cplusplus
 265 typedef logical (*L_fp)(...);
 266 #else
 267 typedef logical (*L_fp)();
 268 #endif
 269
 270 static float spow_ui(float x, integer n) {
 271         float pow=1.0; unsigned long int u;
 272         if(n != 0) {
 273                 if(n < 0) n = -n, x = 1/x;
 274                 for(u = n; ; ) {
 275                         if(u & 01) pow *= x;
 276                         if(u >>= 1) x *= x;
 277                         else break;
 278                 }
 279         }
 280         return pow;
 281 }
 282 static double dpow_ui(double x, integer n) {
 283         double pow=1.0; unsigned long int u;
 284         if(n != 0) {
 285                 if(n < 0) n = -n, x = 1/x;
 286                 for(u = n; ; ) {
 287                         if(u & 01) pow *= x;
 288                         if(u >>= 1) x *= x;
 289                         else break;
 290                 }
 291         }
 292         return pow;
 293 }
 294 #ifdef _MSC_VER
 295 static _Fcomplex cpow_ui(complex x, integer n) {
 296         complex pow={1.0,0.0}; unsigned long int u;
 297                 if(n != 0) {
 298                 if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
 299                 for(u = n; ; ) {
 300                         if(u & 01) pow.r *= x.r, pow.i *= x.i;
 301                         if(u >>= 1) x.r *= x.r, x.i *= x.i;
 302                         else break;
 303                 }
 304         }
 305         _Fcomplex p={pow.r, pow.i};
 306         return p;
 307 }
 308 #else
 309 static _Complex float cpow_ui(_Complex float x, integer n) {
 310         _Complex float pow=1.0; unsigned long int u;
 311         if(n != 0) {
 312                 if(n < 0) n = -n, x = 1/x;
 313                 for(u = n; ; ) {
 314                         if(u & 01) pow *= x;
 315                         if(u >>= 1) x *= x;
 316                         else break;
 317                 }
 318         }
 319         return pow;
 320 }
 321 #endif
 322 #ifdef _MSC_VER
 323 static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
 324         _Dcomplex pow={1.0,0.0}; unsigned long int u;
 325         if(n != 0) {
 326                 if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
 327                 for(u = n; ; ) {
 328                         if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
 329                         if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
 330                         else break;
 331                 }
 332         }
 333         _Dcomplex p = {pow._Val[0], pow._Val[1]};
 334         return p;
 335 }
 336 #else
 337 static _Complex double zpow_ui(_Complex double x, integer n) {
 338         _Complex double pow=1.0; unsigned long int u;
 339         if(n != 0) {
 340                 if(n < 0) n = -n, x = 1/x;
 341                 for(u = n; ; ) {
 342                         if(u & 01) pow *= x;
 343                         if(u >>= 1) x *= x;
 344                         else break;
 345                 }
 346         }
 347         return pow;
 348 }
 349 #endif
 350 static integer pow_ii(integer x, integer n) {
 351         integer pow; unsigned long int u;
 352         if (n <= 0) {
 353                 if (n == 0 || x == 1) pow = 1;
 354                 else if (x != -1) pow = x == 0 ? 1/x : 0;
 355                 else n = -n;
 356         }
 357         if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
 358                 u = n;
 359                 for(pow = 1; ; ) {
 360                         if(u & 01) pow *= x;
 361                         if(u >>= 1) x *= x;
 362                         else break;
 363                 }
 364         }
 365         return pow;
 366 }
 367 static integer dmaxloc_(double *w, integer s, integer e, integer *n)
 368 {
 369         double m; integer i, mi;
 370         for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
 371                 if (w[i-1]>m) mi=i ,m=w[i-1];
 372         return mi-s+1;
 373 }
 374 static integer smaxloc_(float *w, integer s, integer e, integer *n)
 375 {
 376         float m; integer i, mi;
 377         for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
 378                 if (w[i-1]>m) mi=i ,m=w[i-1];
 379         return mi-s+1;
 380 }
 381 static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
 382         integer n = *n_, incx = *incx_, incy = *incy_, i;
 383 #ifdef _MSC_VER
 384         _Fcomplex zdotc = {0.0, 0.0};
 385         if (incx == 1 && incy == 1) {
 386                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 387                         zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
 388                         zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
 389                 }
 390         } else {
 391                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 392                         zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
 393                         zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
 394                 }
 395         }
 396         pCf(z) = zdotc;
 397 }
 398 #else
 399         _Complex float zdotc = 0.0;
 400         if (incx == 1 && incy == 1) {
 401                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 402                         zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
 403                 }
 404         } else {
 405                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 406                         zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
 407                 }
 408         }
 409         pCf(z) = zdotc;
 410 }
 411 #endif
 412 static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
 413         integer n = *n_, incx = *incx_, incy = *incy_, i;
 414 #ifdef _MSC_VER
 415         _Dcomplex zdotc = {0.0, 0.0};
 416         if (incx == 1 && incy == 1) {
 417                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 418                         zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
 419                         zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
 420                 }
 421         } else {
 422                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 423                         zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
 424                         zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
 425                 }
 426         }
 427         pCd(z) = zdotc;
 428 }
 429 #else
 430         _Complex double zdotc = 0.0;
 431         if (incx == 1 && incy == 1) {
 432                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 433                         zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
 434                 }
 435         } else {
 436                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 437                         zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
 438                 }
 439         }
 440         pCd(z) = zdotc;
 441 }
 442 #endif
 443 static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
 444         integer n = *n_, incx = *incx_, incy = *incy_, i;
 445 #ifdef _MSC_VER
 446         _Fcomplex zdotc = {0.0, 0.0};
 447         if (incx == 1 && incy == 1) {
 448                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 449                         zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
 450                         zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
 451                 }
 452         } else {
 453                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 454                         zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
 455                         zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
 456                 }
 457         }
 458         pCf(z) = zdotc;
 459 }
 460 #else
 461         _Complex float zdotc = 0.0;
 462         if (incx == 1 && incy == 1) {
 463                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 464                         zdotc += Cf(&x[i]) * Cf(&y[i]);
 465                 }
 466         } else {
 467                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 468                         zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
 469                 }
 470         }
 471         pCf(z) = zdotc;
 472 }
 473 #endif
 474 static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
 475         integer n = *n_, incx = *incx_, incy = *incy_, i;
 476 #ifdef _MSC_VER
 477         _Dcomplex zdotc = {0.0, 0.0};
 478         if (incx == 1 && incy == 1) {
 479                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 480                         zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
 481                         zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
 482                 }
 483         } else {
 484                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 485                         zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
 486                         zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
 487                 }
 488         }
 489         pCd(z) = zdotc;
 490 }
 491 #else
 492         _Complex double zdotc = 0.0;
 493         if (incx == 1 && incy == 1) {
 494                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 495                         zdotc += Cd(&x[i]) * Cd(&y[i]);
 496                 }
 497         } else {
 498                 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
 499                         zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
 500                 }
 501         }
 502         pCd(z) = zdotc;
 503 }
 504 #endif
 505 /*  -- translated by f2c (version 20000121).
 506    You must link the resulting object file with the libraries:
 507         -lf2c -lm   (in that order)
 508 */
 509
 510
 511
 512
 513 /* Table of constant values */
 514
 515 static integer c__1 = 1;
 516 static integer c__0 = 0;
 517 static real c_b27 = 1.f;
 518
 519 /* > \brief \b CGSVJ0 pre-processor for the routine cgesvj. */
 520
 521 /*  =========== DOCUMENTATION =========== */
 522
 523 /* Online html documentation available at */
 524 /*            http://www.netlib.org/lapack/explore-html/ */
 525
 526 /* > \htmlonly */
 527 /* > Download CGSVJ0 + dependencies */
 528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgsvj0.
 529 f"> */
 530 /* > [TGZ]</a> */
 531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgsvj0.
 532 f"> */
 533 /* > [ZIP]</a> */
 534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgsvj0.
 535 f"> */
 536 /* > [TXT]</a> */
 537 /* > \endhtmlonly */
 538
 539 /*  Definition: */
 540 /*  =========== */
 541
 542 /*       SUBROUTINE CGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, */
 543 /*                          SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) */
 544
 545 /*       INTEGER            INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP */
 546 /*       REAL               EPS, SFMIN, TOL */
 547 /*       CHARACTER*1        JOBV */
 548 /*       COMPLEX            A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK ) */
 549 /*       REAL               SVA( N ) */
 550
 551
 552 /* > \par Purpose: */
 553 /*  ============= */
 554 /* > */
 555 /* > \verbatim */
 556 /* > */
 557 /* > CGSVJ0 is called from CGESVJ as a pre-processor and that is its main */
 558 /* > purpose. It applies Jacobi rotations in the same way as CGESVJ does, but */
 559 /* > it does not check convergence (stopping criterion). Few tuning */
 560 /* > parameters (marked by [TP]) are available for the implementer. */
 561 /* > \endverbatim */
 562
 563 /*  Arguments: */
 564 /*  ========== */
 565
 566 /* > \param[in] JOBV */
 567 /* > \verbatim */
 568 /* >          JOBV is CHARACTER*1 */
 569 /* >          Specifies whether the output from this procedure is used */
 570 /* >          to compute the matrix V: */
 571 /* >          = 'V': the product of the Jacobi rotations is accumulated */
 572 /* >                 by postmulyiplying the N-by-N array V. */
 573 /* >                (See the description of V.) */
 574 /* >          = 'A': the product of the Jacobi rotations is accumulated */
 575 /* >                 by postmulyiplying the MV-by-N array V. */
 576 /* >                (See the descriptions of MV and V.) */
 577 /* >          = 'N': the Jacobi rotations are not accumulated. */
 578 /* > \endverbatim */
 579 /* > */
 580 /* > \param[in] M */
 581 /* > \verbatim */
 582 /* >          M is INTEGER */
 583 /* >          The number of rows of the input matrix A.  M >= 0. */
 584 /* > \endverbatim */
 585 /* > */
 586 /* > \param[in] N */
 587 /* > \verbatim */
 588 /* >          N is INTEGER */
 589 /* >          The number of columns of the input matrix A. */
 590 /* >          M >= N >= 0. */
 591 /* > \endverbatim */
 592 /* > */
 593 /* > \param[in,out] A */
 594 /* > \verbatim */
 595 /* >          A is COMPLEX array, dimension (LDA,N) */
 596 /* >          On entry, M-by-N matrix A, such that A*diag(D) represents */
 597 /* >          the input matrix. */
 598 /* >          On exit, */
 599 /* >          A_onexit * diag(D_onexit) represents the input matrix A*diag(D) */
 600 /* >          post-multiplied by a sequence of Jacobi rotations, where the */
 601 /* >          rotation threshold and the total number of sweeps are given in */
 602 /* >          TOL and NSWEEP, respectively. */
 603 /* >          (See the descriptions of D, TOL and NSWEEP.) */
 604 /* > \endverbatim */
 605 /* > */
 606 /* > \param[in] LDA */
 607 /* > \verbatim */
 608 /* >          LDA is INTEGER */
 609 /* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
 610 /* > \endverbatim */
 611 /* > */
 612 /* > \param[in,out] D */
 613 /* > \verbatim */
 614 /* >          D is COMPLEX array, dimension (N) */
 615 /* >          The array D accumulates the scaling factors from the complex scaled */
 616 /* >          Jacobi rotations. */
 617 /* >          On entry, A*diag(D) represents the input matrix. */
 618 /* >          On exit, A_onexit*diag(D_onexit) represents the input matrix */
 619 /* >          post-multiplied by a sequence of Jacobi rotations, where the */
 620 /* >          rotation threshold and the total number of sweeps are given in */
 621 /* >          TOL and NSWEEP, respectively. */
 622 /* >          (See the descriptions of A, TOL and NSWEEP.) */
 623 /* > \endverbatim */
 624 /* > */
 625 /* > \param[in,out] SVA */
 626 /* > \verbatim */
 627 /* >          SVA is REAL array, dimension (N) */
 628 /* >          On entry, SVA contains the Euclidean norms of the columns of */
 629 /* >          the matrix A*diag(D). */
 630 /* >          On exit, SVA contains the Euclidean norms of the columns of */
 631 /* >          the matrix A_onexit*diag(D_onexit). */
 632 /* > \endverbatim */
 633 /* > */
 634 /* > \param[in] MV */
 635 /* > \verbatim */
 636 /* >          MV is INTEGER */
 637 /* >          If JOBV = 'A', then MV rows of V are post-multipled by a */
 638 /* >                           sequence of Jacobi rotations. */
 639 /* >          If JOBV = 'N',   then MV is not referenced. */
 640 /* > \endverbatim */
 641 /* > */
 642 /* > \param[in,out] V */
 643 /* > \verbatim */
 644 /* >          V is COMPLEX array, dimension (LDV,N) */
 645 /* >          If JOBV = 'V' then N rows of V are post-multipled by a */
 646 /* >                           sequence of Jacobi rotations. */
 647 /* >          If JOBV = 'A' then MV rows of V are post-multipled by a */
 648 /* >                           sequence of Jacobi rotations. */
 649 /* >          If JOBV = 'N',   then V is not referenced. */
 650 /* > \endverbatim */
 651 /* > */
 652 /* > \param[in] LDV */
 653 /* > \verbatim */
 654 /* >          LDV is INTEGER */
 655 /* >          The leading dimension of the array V,  LDV >= 1. */
 656 /* >          If JOBV = 'V', LDV >= N. */
 657 /* >          If JOBV = 'A', LDV >= MV. */
 658 /* > \endverbatim */
 659 /* > */
 660 /* > \param[in] EPS */
 661 /* > \verbatim */
 662 /* >          EPS is REAL */
 663 /* >          EPS = SLAMCH('Epsilon') */
 664 /* > \endverbatim */
 665 /* > */
 666 /* > \param[in] SFMIN */
 667 /* > \verbatim */
 668 /* >          SFMIN is REAL */
 669 /* >          SFMIN = SLAMCH('Safe Minimum') */
 670 /* > \endverbatim */
 671 /* > */
 672 /* > \param[in] TOL */
 673 /* > \verbatim */
 674 /* >          TOL is REAL */
 675 /* >          TOL is the threshold for Jacobi rotations. For a pair */
 676 /* >          A(:,p), A(:,q) of pivot columns, the Jacobi rotation is */
 677 /* >          applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL. */
 678 /* > \endverbatim */
 679 /* > */
 680 /* > \param[in] NSWEEP */
 681 /* > \verbatim */
 682 /* >          NSWEEP is INTEGER */
 683 /* >          NSWEEP is the number of sweeps of Jacobi rotations to be */
 684 /* >          performed. */
 685 /* > \endverbatim */
 686 /* > */
 687 /* > \param[out] WORK */
 688 /* > \verbatim */
 689 /* >          WORK is COMPLEX array, dimension (LWORK) */
 690 /* > \endverbatim */
 691 /* > */
 692 /* > \param[in] LWORK */
 693 /* > \verbatim */
 694 /* >          LWORK is INTEGER */
 695 /* >          LWORK is the dimension of WORK. LWORK >= M. */
 696 /* > \endverbatim */
 697 /* > */
 698 /* > \param[out] INFO */
 699 /* > \verbatim */
 700 /* >          INFO is INTEGER */
 701 /* >          = 0:  successful exit. */
 702 /* >          < 0:  if INFO = -i, then the i-th argument had an illegal value */
 703 /* > \endverbatim */
 704
 705 /*  Authors: */
 706 /*  ======== */
 707
 708 /* > \author Univ. of Tennessee */
 709 /* > \author Univ. of California Berkeley */
 710 /* > \author Univ. of Colorado Denver */
 711 /* > \author NAG Ltd. */
 712
 713 /* > \date June 2016 */
 714
 715 /* > \ingroup complexOTHERcomputational */
 716
 717 /* > \par Further Details: */
 718 /*  ===================== */
 719 /* > */
 720 /* > CGSVJ0 is used just to enable CGESVJ to call a simplified version of */
 721 /* > itself to work on a submatrix of the original matrix. */
 722 /* > */
 723 /* > \par Contributor: */
 724 /*  ================== */
 725 /* > */
 726 /* > Zlatko Drmac (Zagreb, Croatia) */
 727 /* > */
 728 /* > \par Bugs, Examples and Comments: */
 729 /*  ================================= */
 730 /* > */
 731 /* > Please report all bugs and send interesting test examples and comments to */
 732 /* > drmac@math.hr. Thank you. */
 733
 734 /*  ===================================================================== */
 735 /* Subroutine */ int cgsvj0_(char *jobv, integer *m, integer *n, complex *a,
 736         integer *lda, complex *d__, real *sva, integer *mv, complex *v,
 737         integer *ldv, real *eps, real *sfmin, real *tol, integer *nsweep,
 738         complex *work, integer *lwork, integer *info)
 739 {
 740     /* System generated locals */
 741     integer a_dim1, a_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5,
 742             i__6, i__7;
 743     real r__1, r__2;
 744     complex q__1, q__2, q__3;
 745
 746     /* Local variables */
 747     real aapp;
 748     complex aapq;
 749     real aaqq;
 750     integer ierr;
 751     real bigtheta;
 752     extern /* Subroutine */ int crot_(integer *, complex *, integer *,
 753             complex *, integer *, real *, complex *);
 754     complex ompq;
 755     integer pskipped;
 756     real aapp0, aapq1, temp1;
 757     integer i__, p, q;
 758     real t;
 759     extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
 760             *, complex *, integer *);
 761     real apoaq, aqoap;
 762     extern logical lsame_(char *, char *);
 763     real theta, small;
 764     extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
 765             complex *, integer *), cswap_(integer *, complex *, integer *,
 766             complex *, integer *);
 767     logical applv, rsvec;
 768     extern /* Subroutine */ int caxpy_(integer *, complex *, complex *,
 769             integer *, complex *, integer *);
 770     logical rotok;
 771     real rootsfmin;
 772     extern real scnrm2_(integer *, complex *, integer *);
 773     real cs, sn;
 774     extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *,
 775             real *, integer *, integer *, complex *, integer *, integer *), xerbla_(char *, integer *, ftnlen);
 776     integer ijblsk, swband;
 777     extern integer isamax_(integer *, real *, integer *);
 778     integer blskip;
 779     extern /* Subroutine */ int classq_(integer *, complex *, integer *, real
 780             *, real *);
 781     real mxaapq, thsign, mxsinj;
 782     integer ir1, emptsw, notrot, iswrot, jbc;
 783     real big;
 784     integer kbl, lkahead, igl, ibr, jgl, nbl, mvl;
 785     real rootbig, rooteps;
 786     integer rowskip;
 787     real roottol;
 788
 789
 790 /*  -- LAPACK computational routine (version 3.8.0) -- */
 791 /*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
 792 /*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
 793 /*     June 2016 */
 794
 795
 796 /*  ===================================================================== */
 797
 798 /*     from BLAS */
 799 /*     from LAPACK */
 800
 801 /*     Test the input parameters. */
 802
 803     /* Parameter adjustments */
 804     --sva;
 805     --d__;
 806     a_dim1 = *lda;
 807     a_offset = 1 + a_dim1 * 1;
 808     a -= a_offset;
 809     v_dim1 = *ldv;
 810     v_offset = 1 + v_dim1 * 1;
 811     v -= v_offset;
 812     --work;
 813
 814     /* Function Body */
 815     applv = lsame_(jobv, "A");
 816     rsvec = lsame_(jobv, "V");
 817     if (! (rsvec || applv || lsame_(jobv, "N"))) {
 818         *info = -1;
 819     } else if (*m < 0) {
 820         *info = -2;
 821     } else if (*n < 0 || *n > *m) {
 822         *info = -3;
 823     } else if (*lda < *m) {
 824         *info = -5;
 825     } else if ((rsvec || applv) && *mv < 0) {
 826         *info = -8;
 827     } else if (rsvec && *ldv < *n || applv && *ldv < *mv) {
 828         *info = -10;
 829     } else if (*tol <= *eps) {
 830         *info = -13;
 831     } else if (*nsweep < 0) {
 832         *info = -14;
 833     } else if (*lwork < *m) {
 834         *info = -16;
 835     } else {
 836         *info = 0;
 837     }
 838
 839 /*     #:( */
 840     if (*info != 0) {
 841         i__1 = -(*info);
 842         xerbla_("CGSVJ0", &i__1, (ftnlen)6);
 843         return 0;
 844     }
 845
 846     if (rsvec) {
 847         mvl = *n;
 848     } else if (applv) {
 849         mvl = *mv;
 850     }
 851     rsvec = rsvec || applv;
 852     rooteps = sqrt(*eps);
 853     rootsfmin = sqrt(*sfmin);
 854     small = *sfmin / *eps;
 855     big = 1.f / *sfmin;
 856     rootbig = 1.f / rootsfmin;
 857     bigtheta = 1.f / rooteps;
 858     roottol = sqrt(*tol);
 859
 860
 861     emptsw = *n * (*n - 1) / 2;
 862     notrot = 0;
 863
 864
 865     swband = 0;
 866 /* [TP] SWBAND is a tuning parameter [TP]. It is meaningful and effective */
 867 /*     if CGESVJ is used as a computational routine in the preconditioned */
 868 /*     Jacobi SVD algorithm CGEJSV. For sweeps i=1:SWBAND the procedure */
 869 /*     works on pivots inside a band-like region around the diagonal. */
 870 /*     The boundaries are determined dynamically, based on the number of */
 871 /*     pivots above a threshold. */
 872
 873     kbl = f2cmin(8,*n);
 874 /* [TP] KBL is a tuning parameter that defines the tile size in the */
 875 /*     tiling of the p-q loops of pivot pairs. In general, an optimal */
 876 /*     value of KBL depends on the matrix dimensions and on the */
 877 /*     parameters of the computer's memory. */
 878
 879     nbl = *n / kbl;
 880     if (nbl * kbl != *n) {
 881         ++nbl;
 882     }
 883
 884 /* Computing 2nd power */
 885     i__1 = kbl;
 886     blskip = i__1 * i__1;
 887 /* [TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. */
 888
 889     rowskip = f2cmin(5,kbl);
 890 /* [TP] ROWSKIP is a tuning parameter. */
 891
 892     lkahead = 1;
 893 /* [TP] LKAHEAD is a tuning parameter. */
 894
 895 /*     Quasi block transformations, using the lower (upper) triangular */
 896 /*     structure of the input matrix. The quasi-block-cycling usually */
 897 /*     invokes cubic convergence. Big part of this cycle is done inside */
 898 /*     canonical subspaces of dimensions less than M. */
 899
 900
 901
 902     i__1 = *nsweep;
 903     for (i__ = 1; i__ <= i__1; ++i__) {
 904
 905
 906         mxaapq = 0.f;
 907         mxsinj = 0.f;
 908         iswrot = 0;
 909
 910         notrot = 0;
 911         pskipped = 0;
 912
 913 /*     Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs */
 914 /*     1 <= p < q <= N. This is the first step toward a blocked implementation */
 915 /*     of the rotations. New implementation, based on block transformations, */
 916 /*     is under development. */
 917
 918         i__2 = nbl;
 919         for (ibr = 1; ibr <= i__2; ++ibr) {
 920
 921             igl = (ibr - 1) * kbl + 1;
 922
 923 /* Computing MIN */
 924             i__4 = lkahead, i__5 = nbl - ibr;
 925             i__3 = f2cmin(i__4,i__5);
 926             for (ir1 = 0; ir1 <= i__3; ++ir1) {
 927
 928                 igl += ir1 * kbl;
 929
 930 /* Computing MIN */
 931                 i__5 = igl + kbl - 1, i__6 = *n - 1;
 932                 i__4 = f2cmin(i__5,i__6);
 933                 for (p = igl; p <= i__4; ++p) {
 934
 935
 936                     i__5 = *n - p + 1;
 937                     q = isamax_(&i__5, &sva[p], &c__1) + p - 1;
 938                     if (p != q) {
 939                         cswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 +
 940                                 1], &c__1);
 941                         if (rsvec) {
 942                             cswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
 943                                     v_dim1 + 1], &c__1);
 944                         }
 945                         temp1 = sva[p];
 946                         sva[p] = sva[q];
 947                         sva[q] = temp1;
 948                         i__5 = p;
 949                         aapq.r = d__[i__5].r, aapq.i = d__[i__5].i;
 950                         i__5 = p;
 951                         i__6 = q;
 952                         d__[i__5].r = d__[i__6].r, d__[i__5].i = d__[i__6].i;
 953                         i__5 = q;
 954                         d__[i__5].r = aapq.r, d__[i__5].i = aapq.i;
 955                     }
 956
 957                     if (ir1 == 0) {
 958
 959 /*        Column norms are periodically updated by explicit */
 960 /*        norm computation. */
 961 /*        Caveat: */
 962 /*        Unfortunately, some BLAS implementations compute SNCRM2(M,A(1,p),1) */
 963 /*        as SQRT(S=CDOTC(M,A(1,p),1,A(1,p),1)), which may cause the result to */
 964 /*        overflow for ||A(:,p)||_2 > SQRT(overflow_threshold), and to */
 965 /*        underflow for ||A(:,p)||_2 < SQRT(underflow_threshold). */
 966 /*        Hence, SCNRM2 cannot be trusted, not even in the case when */
 967 /*        the true norm is far from the under(over)flow boundaries. */
 968 /*        If properly implemented SCNRM2 is available, the IF-THEN-ELSE-END IF */
 969 /*        below should be replaced with "AAPP = SCNRM2( M, A(1,p), 1 )". */
 970
 971                         if (sva[p] < rootbig && sva[p] > rootsfmin) {
 972                             sva[p] = scnrm2_(m, &a[p * a_dim1 + 1], &c__1);
 973                         } else {
 974                             temp1 = 0.f;
 975                             aapp = 1.f;
 976                             classq_(m, &a[p * a_dim1 + 1], &c__1, &temp1, &
 977                                     aapp);
 978                             sva[p] = temp1 * sqrt(aapp);
 979                         }
 980                         aapp = sva[p];
 981                     } else {
 982                         aapp = sva[p];
 983                     }
 984
 985                     if (aapp > 0.f) {
 986
 987                         pskipped = 0;
 988
 989 /* Computing MIN */
 990                         i__6 = igl + kbl - 1;
 991                         i__5 = f2cmin(i__6,*n);
 992                         for (q = p + 1; q <= i__5; ++q) {
 993
 994                             aaqq = sva[q];
 995
 996                             if (aaqq > 0.f) {
 997
 998                                 aapp0 = aapp;
 999                                 if (aaqq >= 1.f) {
1000                                     rotok = small * aapp <= aaqq;
1001                                     if (aapp < big / aaqq) {
1002                                         cdotc_(&q__3, m, &a[p * a_dim1 + 1], &
1003                                                 c__1, &a[q * a_dim1 + 1], &
1004                                                 c__1);
1005                                         q__2.r = q__3.r / aaqq, q__2.i =
1006                                                 q__3.i / aaqq;
1007                                         q__1.r = q__2.r / aapp, q__1.i =
1008                                                 q__2.i / aapp;
1009                                         aapq.r = q__1.r, aapq.i = q__1.i;
1010                                     } else {
1011                                         ccopy_(m, &a[p * a_dim1 + 1], &c__1, &
1012                                                 work[1], &c__1);
1013                                         clascl_("G", &c__0, &c__0, &aapp, &
1014                                                 c_b27, m, &c__1, &work[1],
1015                                                 lda, &ierr);
1016                                         cdotc_(&q__2, m, &work[1], &c__1, &a[
1017                                                 q * a_dim1 + 1], &c__1);
1018                                         q__1.r = q__2.r / aaqq, q__1.i =
1019                                                 q__2.i / aaqq;
1020                                         aapq.r = q__1.r, aapq.i = q__1.i;
1021                                     }
1022                                 } else {
1023                                     rotok = aapp <= aaqq / small;
1024                                     if (aapp > small / aaqq) {
1025                                         cdotc_(&q__3, m, &a[p * a_dim1 + 1], &
1026                                                 c__1, &a[q * a_dim1 + 1], &
1027                                                 c__1);
1028                                         q__2.r = q__3.r / aapp, q__2.i =
1029                                                 q__3.i / aapp;
1030                                         q__1.r = q__2.r / aaqq, q__1.i =
1031                                                 q__2.i / aaqq;
1032                                         aapq.r = q__1.r, aapq.i = q__1.i;
1033                                     } else {
1034                                         ccopy_(m, &a[q * a_dim1 + 1], &c__1, &
1035                                                 work[1], &c__1);
1036                                         clascl_("G", &c__0, &c__0, &aaqq, &
1037                                                 c_b27, m, &c__1, &work[1],
1038                                                 lda, &ierr);
1039                                         cdotc_(&q__2, m, &a[p * a_dim1 + 1], &
1040                                                 c__1, &work[1], &c__1);
1041                                         q__1.r = q__2.r / aapp, q__1.i =
1042                                                 q__2.i / aapp;
1043                                         aapq.r = q__1.r, aapq.i = q__1.i;
1044                                     }
1045                                 }
1046
1047 /*                           AAPQ = AAPQ * CONJG( CWORK(p) ) * CWORK(q) */
1048                                 aapq1 = -c_abs(&aapq);
1049 /* Computing MAX */
1050                                 r__1 = mxaapq, r__2 = -aapq1;
1051                                 mxaapq = f2cmax(r__1,r__2);
1052
1053 /*        TO rotate or NOT to rotate, THAT is the question ... */
1054
1055                                 if (abs(aapq1) > *tol) {
1056                                     r__1 = c_abs(&aapq);
1057                                     q__1.r = aapq.r / r__1, q__1.i = aapq.i /
1058                                             r__1;
1059                                     ompq.r = q__1.r, ompq.i = q__1.i;
1060
1061 /* [RTD]      ROTATED = ROTATED + ONE */
1062
1063                                     if (ir1 == 0) {
1064                                         notrot = 0;
1065                                         pskipped = 0;
1066                                         ++iswrot;
1067                                     }
1068
1069                                     if (rotok) {
1070
1071                                         aqoap = aaqq / aapp;
1072                                         apoaq = aapp / aaqq;
1073                                         theta = (r__1 = aqoap - apoaq, abs(
1074                                                 r__1)) * -.5f / aapq1;
1075
1076                                         if (abs(theta) > bigtheta) {
1077
1078                                             t = .5f / theta;
1079                                             cs = 1.f;
1080                                             r_cnjg(&q__2, &ompq);
1081                                             q__1.r = t * q__2.r, q__1.i = t *
1082                                                     q__2.i;
1083                                             crot_(m, &a[p * a_dim1 + 1], &
1084                                                     c__1, &a[q * a_dim1 + 1],
1085                                                     &c__1, &cs, &q__1);
1086                                             if (rsvec) {
1087                           r_cnjg(&q__2, &ompq);
1088                           q__1.r = t * q__2.r, q__1.i = t * q__2.i;
1089                           crot_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
1090                                   v_dim1 + 1], &c__1, &cs, &q__1);
1091                                             }
1092 /* Computing MAX */
1093                                             r__1 = 0.f, r__2 = t * apoaq *
1094                                                     aapq1 + 1.f;
1095                                             sva[q] = aaqq * sqrt((f2cmax(r__1,
1096                                                     r__2)));
1097 /* Computing MAX */
1098                                             r__1 = 0.f, r__2 = 1.f - t *
1099                                                     aqoap * aapq1;
1100                                             aapp *= sqrt((f2cmax(r__1,r__2)));
1101 /* Computing MAX */
1102                                             r__1 = mxsinj, r__2 = abs(t);
1103                                             mxsinj = f2cmax(r__1,r__2);
1104
1105                                         } else {
1106
1107
1108                                             thsign = -r_sign(&c_b27, &aapq1);
1109                                             t = 1.f / (theta + thsign * sqrt(
1110                                                     theta * theta + 1.f));
1111                                             cs = sqrt(1.f / (t * t + 1.f));
1112                                             sn = t * cs;
1113
1114 /* Computing MAX */
1115                                             r__1 = mxsinj, r__2 = abs(sn);
1116                                             mxsinj = f2cmax(r__1,r__2);
1117 /* Computing MAX */
1118                                             r__1 = 0.f, r__2 = t * apoaq *
1119                                                     aapq1 + 1.f;
1120                                             sva[q] = aaqq * sqrt((f2cmax(r__1,
1121                                                     r__2)));
1122 /* Computing MAX */
1123                                             r__1 = 0.f, r__2 = 1.f - t *
1124                                                     aqoap * aapq1;
1125                                             aapp *= sqrt((f2cmax(r__1,r__2)));
1126
1127                                             r_cnjg(&q__2, &ompq);
1128                                             q__1.r = sn * q__2.r, q__1.i = sn
1129                                                     * q__2.i;
1130                                             crot_(m, &a[p * a_dim1 + 1], &
1131                                                     c__1, &a[q * a_dim1 + 1],
1132                                                     &c__1, &cs, &q__1);
1133                                             if (rsvec) {
1134                           r_cnjg(&q__2, &ompq);
1135                           q__1.r = sn * q__2.r, q__1.i = sn * q__2.i;
1136                           crot_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
1137                                   v_dim1 + 1], &c__1, &cs, &q__1);
1138                                             }
1139                                         }
1140                                         i__6 = p;
1141                                         i__7 = q;
1142                                         q__2.r = -d__[i__7].r, q__2.i = -d__[
1143                                                 i__7].i;
1144                                         q__1.r = q__2.r * ompq.r - q__2.i *
1145                                                 ompq.i, q__1.i = q__2.r *
1146                                                 ompq.i + q__2.i * ompq.r;
1147                                         d__[i__6].r = q__1.r, d__[i__6].i =
1148                                                 q__1.i;
1149
1150                                     } else {
1151                                         ccopy_(m, &a[p * a_dim1 + 1], &c__1, &
1152                                                 work[1], &c__1);
1153                                         clascl_("G", &c__0, &c__0, &aapp, &
1154                                                 c_b27, m, &c__1, &work[1],
1155                                                 lda, &ierr);
1156                                         clascl_("G", &c__0, &c__0, &aaqq, &
1157                                                 c_b27, m, &c__1, &a[q *
1158                                                 a_dim1 + 1], lda, &ierr);
1159                                         q__1.r = -aapq.r, q__1.i = -aapq.i;
1160                                         caxpy_(m, &q__1, &work[1], &c__1, &a[
1161                                                 q * a_dim1 + 1], &c__1);
1162                                         clascl_("G", &c__0, &c__0, &c_b27, &
1163                                                 aaqq, m, &c__1, &a[q * a_dim1
1164                                                 + 1], lda, &ierr);
1165 /* Computing MAX */
1166                                         r__1 = 0.f, r__2 = 1.f - aapq1 *
1167                                                 aapq1;
1168                                         sva[q] = aaqq * sqrt((f2cmax(r__1,r__2)))
1169                                                 ;
1170                                         mxsinj = f2cmax(mxsinj,*sfmin);
1171                                     }
1172 /*           END IF ROTOK THEN ... ELSE */
1173
1174 /*           In the case of cancellation in updating SVA(q), SVA(p) */
1175 /*           recompute SVA(q), SVA(p). */
1176
1177 /* Computing 2nd power */
1178                                     r__1 = sva[q] / aaqq;
1179                                     if (r__1 * r__1 <= rooteps) {
1180                                         if (aaqq < rootbig && aaqq >
1181                                                 rootsfmin) {
1182                                             sva[q] = scnrm2_(m, &a[q * a_dim1
1183                                                     + 1], &c__1);
1184                                         } else {
1185                                             t = 0.f;
1186                                             aaqq = 1.f;
1187                                             classq_(m, &a[q * a_dim1 + 1], &
1188                                                     c__1, &t, &aaqq);
1189                                             sva[q] = t * sqrt(aaqq);
1190                                         }
1191                                     }
1192                                     if (aapp / aapp0 <= rooteps) {
1193                                         if (aapp < rootbig && aapp >
1194                                                 rootsfmin) {
1195                                             aapp = scnrm2_(m, &a[p * a_dim1 +
1196                                                     1], &c__1);
1197                                         } else {
1198                                             t = 0.f;
1199                                             aapp = 1.f;
1200                                             classq_(m, &a[p * a_dim1 + 1], &
1201                                                     c__1, &t, &aapp);
1202                                             aapp = t * sqrt(aapp);
1203                                         }
1204                                         sva[p] = aapp;
1205                                     }
1206
1207                                 } else {
1208 /*        A(:,p) and A(:,q) already numerically orthogonal */
1209                                     if (ir1 == 0) {
1210                                         ++notrot;
1211                                     }
1212 /* [RTD]      SKIPPED  = SKIPPED  + 1 */
1213                                     ++pskipped;
1214                                 }
1215                             } else {
1216 /*        A(:,q) is zero column */
1217                                 if (ir1 == 0) {
1218                                     ++notrot;
1219                                 }
1220                                 ++pskipped;
1221                             }
1222
1223                             if (i__ <= swband && pskipped > rowskip) {
1224                                 if (ir1 == 0) {
1225                                     aapp = -aapp;
1226                                 }
1227                                 notrot = 0;
1228                                 goto L2103;
1229                             }
1230
1231 /* L2002: */
1232                         }
1233 /*     END q-LOOP */
1234
1235 L2103:
1236 /*     bailed out of q-loop */
1237
1238                         sva[p] = aapp;
1239
1240                     } else {
1241                         sva[p] = aapp;
1242                         if (ir1 == 0 && aapp == 0.f) {
1243 /* Computing MIN */
1244                             i__5 = igl + kbl - 1;
1245                             notrot = notrot + f2cmin(i__5,*n) - p;
1246                         }
1247                     }
1248
1249 /* L2001: */
1250                 }
1251 /*     end of the p-loop */
1252 /*     end of doing the block ( ibr, ibr ) */
1253 /* L1002: */
1254             }
1255 /*     end of ir1-loop */
1256
1257 /* ... go to the off diagonal blocks */
1258
1259             igl = (ibr - 1) * kbl + 1;
1260
1261             i__3 = nbl;
1262             for (jbc = ibr + 1; jbc <= i__3; ++jbc) {
1263
1264                 jgl = (jbc - 1) * kbl + 1;
1265
1266 /*        doing the block at ( ibr, jbc ) */
1267
1268                 ijblsk = 0;
1269 /* Computing MIN */
1270                 i__5 = igl + kbl - 1;
1271                 i__4 = f2cmin(i__5,*n);
1272                 for (p = igl; p <= i__4; ++p) {
1273
1274                     aapp = sva[p];
1275                     if (aapp > 0.f) {
1276
1277                         pskipped = 0;
1278
1279 /* Computing MIN */
1280                         i__6 = jgl + kbl - 1;
1281                         i__5 = f2cmin(i__6,*n);
1282                         for (q = jgl; q <= i__5; ++q) {
1283
1284                             aaqq = sva[q];
1285                             if (aaqq > 0.f) {
1286                                 aapp0 = aapp;
1287
1288
1289 /*        Safe Gram matrix computation */
1290
1291                                 if (aaqq >= 1.f) {
1292                                     if (aapp >= aaqq) {
1293                                         rotok = small * aapp <= aaqq;
1294                                     } else {
1295                                         rotok = small * aaqq <= aapp;
1296                                     }
1297                                     if (aapp < big / aaqq) {
1298                                         cdotc_(&q__3, m, &a[p * a_dim1 + 1], &
1299                                                 c__1, &a[q * a_dim1 + 1], &
1300                                                 c__1);
1301                                         q__2.r = q__3.r / aaqq, q__2.i =
1302                                                 q__3.i / aaqq;
1303                                         q__1.r = q__2.r / aapp, q__1.i =
1304                                                 q__2.i / aapp;
1305                                         aapq.r = q__1.r, aapq.i = q__1.i;
1306                                     } else {
1307                                         ccopy_(m, &a[p * a_dim1 + 1], &c__1, &
1308                                                 work[1], &c__1);
1309                                         clascl_("G", &c__0, &c__0, &aapp, &
1310                                                 c_b27, m, &c__1, &work[1],
1311                                                 lda, &ierr);
1312                                         cdotc_(&q__2, m, &work[1], &c__1, &a[
1313                                                 q * a_dim1 + 1], &c__1);
1314                                         q__1.r = q__2.r / aaqq, q__1.i =
1315                                                 q__2.i / aaqq;
1316                                         aapq.r = q__1.r, aapq.i = q__1.i;
1317                                     }
1318                                 } else {
1319                                     if (aapp >= aaqq) {
1320                                         rotok = aapp <= aaqq / small;
1321                                     } else {
1322                                         rotok = aaqq <= aapp / small;
1323                                     }
1324                                     if (aapp > small / aaqq) {
1325                                         cdotc_(&q__3, m, &a[p * a_dim1 + 1], &
1326                                                 c__1, &a[q * a_dim1 + 1], &
1327                                                 c__1);
1328                                         r__1 = f2cmax(aaqq,aapp);
1329                                         q__2.r = q__3.r / r__1, q__2.i =
1330                                                 q__3.i / r__1;
1331                                         r__2 = f2cmin(aaqq,aapp);
1332                                         q__1.r = q__2.r / r__2, q__1.i =
1333                                                 q__2.i / r__2;
1334                                         aapq.r = q__1.r, aapq.i = q__1.i;
1335                                     } else {
1336                                         ccopy_(m, &a[q * a_dim1 + 1], &c__1, &
1337                                                 work[1], &c__1);
1338                                         clascl_("G", &c__0, &c__0, &aaqq, &
1339                                                 c_b27, m, &c__1, &work[1],
1340                                                 lda, &ierr);
1341                                         cdotc_(&q__2, m, &a[p * a_dim1 + 1], &
1342                                                 c__1, &work[1], &c__1);
1343                                         q__1.r = q__2.r / aapp, q__1.i =
1344                                                 q__2.i / aapp;
1345                                         aapq.r = q__1.r, aapq.i = q__1.i;
1346                                     }
1347                                 }
1348
1349 /*                           AAPQ = AAPQ * CONJG(CWORK(p))*CWORK(q) */
1350                                 aapq1 = -c_abs(&aapq);
1351 /* Computing MAX */
1352                                 r__1 = mxaapq, r__2 = -aapq1;
1353                                 mxaapq = f2cmax(r__1,r__2);
1354
1355 /*        TO rotate or NOT to rotate, THAT is the question ... */
1356
1357                                 if (abs(aapq1) > *tol) {
1358                                     r__1 = c_abs(&aapq);
1359                                     q__1.r = aapq.r / r__1, q__1.i = aapq.i /
1360                                             r__1;
1361                                     ompq.r = q__1.r, ompq.i = q__1.i;
1362                                     notrot = 0;
1363 /* [RTD]      ROTATED  = ROTATED + 1 */
1364                                     pskipped = 0;
1365                                     ++iswrot;
1366
1367                                     if (rotok) {
1368
1369                                         aqoap = aaqq / aapp;
1370                                         apoaq = aapp / aaqq;
1371                                         theta = (r__1 = aqoap - apoaq, abs(
1372                                                 r__1)) * -.5f / aapq1;
1373                                         if (aaqq > aapp0) {
1374                                             theta = -theta;
1375                                         }
1376
1377                                         if (abs(theta) > bigtheta) {
1378                                             t = .5f / theta;
1379                                             cs = 1.f;
1380                                             r_cnjg(&q__2, &ompq);
1381                                             q__1.r = t * q__2.r, q__1.i = t *
1382                                                     q__2.i;
1383                                             crot_(m, &a[p * a_dim1 + 1], &
1384                                                     c__1, &a[q * a_dim1 + 1],
1385                                                     &c__1, &cs, &q__1);
1386                                             if (rsvec) {
1387                           r_cnjg(&q__2, &ompq);
1388                           q__1.r = t * q__2.r, q__1.i = t * q__2.i;
1389                           crot_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
1390                                   v_dim1 + 1], &c__1, &cs, &q__1);
1391                                             }
1392 /* Computing MAX */
1393                                             r__1 = 0.f, r__2 = t * apoaq *
1394                                                     aapq1 + 1.f;
1395                                             sva[q] = aaqq * sqrt((f2cmax(r__1,
1396                                                     r__2)));
1397 /* Computing MAX */
1398                                             r__1 = 0.f, r__2 = 1.f - t *
1399                                                     aqoap * aapq1;
1400                                             aapp *= sqrt((f2cmax(r__1,r__2)));
1401 /* Computing MAX */
1402                                             r__1 = mxsinj, r__2 = abs(t);
1403                                             mxsinj = f2cmax(r__1,r__2);
1404                                         } else {
1405
1406
1407                                             thsign = -r_sign(&c_b27, &aapq1);
1408                                             if (aaqq > aapp0) {
1409                           thsign = -thsign;
1410                                             }
1411                                             t = 1.f / (theta + thsign * sqrt(
1412                                                     theta * theta + 1.f));
1413                                             cs = sqrt(1.f / (t * t + 1.f));
1414                                             sn = t * cs;
1415 /* Computing MAX */
1416                                             r__1 = mxsinj, r__2 = abs(sn);
1417                                             mxsinj = f2cmax(r__1,r__2);
1418 /* Computing MAX */
1419                                             r__1 = 0.f, r__2 = t * apoaq *
1420                                                     aapq1 + 1.f;
1421                                             sva[q] = aaqq * sqrt((f2cmax(r__1,
1422                                                     r__2)));
1423 /* Computing MAX */
1424                                             r__1 = 0.f, r__2 = 1.f - t *
1425                                                     aqoap * aapq1;
1426                                             aapp *= sqrt((f2cmax(r__1,r__2)));
1427
1428                                             r_cnjg(&q__2, &ompq);
1429                                             q__1.r = sn * q__2.r, q__1.i = sn
1430                                                     * q__2.i;
1431                                             crot_(m, &a[p * a_dim1 + 1], &
1432                                                     c__1, &a[q * a_dim1 + 1],
1433                                                     &c__1, &cs, &q__1);
1434                                             if (rsvec) {
1435                           r_cnjg(&q__2, &ompq);
1436                           q__1.r = sn * q__2.r, q__1.i = sn * q__2.i;
1437                           crot_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
1438                                   v_dim1 + 1], &c__1, &cs, &q__1);
1439                                             }
1440                                         }
1441                                         i__6 = p;
1442                                         i__7 = q;
1443                                         q__2.r = -d__[i__7].r, q__2.i = -d__[
1444                                                 i__7].i;
1445                                         q__1.r = q__2.r * ompq.r - q__2.i *
1446                                                 ompq.i, q__1.i = q__2.r *
1447                                                 ompq.i + q__2.i * ompq.r;
1448                                         d__[i__6].r = q__1.r, d__[i__6].i =
1449                                                 q__1.i;
1450
1451                                     } else {
1452                                         if (aapp > aaqq) {
1453                                             ccopy_(m, &a[p * a_dim1 + 1], &
1454                                                     c__1, &work[1], &c__1);
1455                                             clascl_("G", &c__0, &c__0, &aapp,
1456                                                     &c_b27, m, &c__1, &work[1]
1457                                                     , lda, &ierr);
1458                                             clascl_("G", &c__0, &c__0, &aaqq,
1459                                                     &c_b27, m, &c__1, &a[q *
1460                                                     a_dim1 + 1], lda, &ierr);
1461                                             q__1.r = -aapq.r, q__1.i =
1462                                                     -aapq.i;
1463                                             caxpy_(m, &q__1, &work[1], &c__1,
1464                                                     &a[q * a_dim1 + 1], &c__1)
1465                                                     ;
1466                                             clascl_("G", &c__0, &c__0, &c_b27,
1467                                                      &aaqq, m, &c__1, &a[q *
1468                                                     a_dim1 + 1], lda, &ierr);
1469 /* Computing MAX */
1470                                             r__1 = 0.f, r__2 = 1.f - aapq1 *
1471                                                     aapq1;
1472                                             sva[q] = aaqq * sqrt((f2cmax(r__1,
1473                                                     r__2)));
1474                                             mxsinj = f2cmax(mxsinj,*sfmin);
1475                                         } else {
1476                                             ccopy_(m, &a[q * a_dim1 + 1], &
1477                                                     c__1, &work[1], &c__1);
1478                                             clascl_("G", &c__0, &c__0, &aaqq,
1479                                                     &c_b27, m, &c__1, &work[1]
1480                                                     , lda, &ierr);
1481                                             clascl_("G", &c__0, &c__0, &aapp,
1482                                                     &c_b27, m, &c__1, &a[p *
1483                                                     a_dim1 + 1], lda, &ierr);
1484                                             r_cnjg(&q__2, &aapq);
1485                                             q__1.r = -q__2.r, q__1.i =
1486                                                     -q__2.i;
1487                                             caxpy_(m, &q__1, &work[1], &c__1,
1488                                                     &a[p * a_dim1 + 1], &c__1)
1489                                                     ;
1490                                             clascl_("G", &c__0, &c__0, &c_b27,
1491                                                      &aapp, m, &c__1, &a[p *
1492                                                     a_dim1 + 1], lda, &ierr);
1493 /* Computing MAX */
1494                                             r__1 = 0.f, r__2 = 1.f - aapq1 *
1495                                                     aapq1;
1496                                             sva[p] = aapp * sqrt((f2cmax(r__1,
1497                                                     r__2)));
1498                                             mxsinj = f2cmax(mxsinj,*sfmin);
1499                                         }
1500                                     }
1501 /*           END IF ROTOK THEN ... ELSE */
1502
1503 /*           In the case of cancellation in updating SVA(q), SVA(p) */
1504 /* Computing 2nd power */
1505                                     r__1 = sva[q] / aaqq;
1506                                     if (r__1 * r__1 <= rooteps) {
1507                                         if (aaqq < rootbig && aaqq >
1508                                                 rootsfmin) {
1509                                             sva[q] = scnrm2_(m, &a[q * a_dim1
1510                                                     + 1], &c__1);
1511                                         } else {
1512                                             t = 0.f;
1513                                             aaqq = 1.f;
1514                                             classq_(m, &a[q * a_dim1 + 1], &
1515                                                     c__1, &t, &aaqq);
1516                                             sva[q] = t * sqrt(aaqq);
1517                                         }
1518                                     }
1519 /* Computing 2nd power */
1520                                     r__1 = aapp / aapp0;
1521                                     if (r__1 * r__1 <= rooteps) {
1522                                         if (aapp < rootbig && aapp >
1523                                                 rootsfmin) {
1524                                             aapp = scnrm2_(m, &a[p * a_dim1 +
1525                                                     1], &c__1);
1526                                         } else {
1527                                             t = 0.f;
1528                                             aapp = 1.f;
1529                                             classq_(m, &a[p * a_dim1 + 1], &
1530                                                     c__1, &t, &aapp);
1531                                             aapp = t * sqrt(aapp);
1532                                         }
1533                                         sva[p] = aapp;
1534                                     }
1535 /*              end of OK rotation */
1536                                 } else {
1537                                     ++notrot;
1538 /* [RTD]      SKIPPED  = SKIPPED  + 1 */
1539                                     ++pskipped;
1540                                     ++ijblsk;
1541                                 }
1542                             } else {
1543                                 ++notrot;
1544                                 ++pskipped;
1545                                 ++ijblsk;
1546                             }
1547
1548                             if (i__ <= swband && ijblsk >= blskip) {
1549                                 sva[p] = aapp;
1550                                 notrot = 0;
1551                                 goto L2011;
1552                             }
1553                             if (i__ <= swband && pskipped > rowskip) {
1554                                 aapp = -aapp;
1555                                 notrot = 0;
1556                                 goto L2203;
1557                             }
1558
1559 /* L2200: */
1560                         }
1561 /*        end of the q-loop */
1562 L2203:
1563
1564                         sva[p] = aapp;
1565
1566                     } else {
1567
1568                         if (aapp == 0.f) {
1569 /* Computing MIN */
1570                             i__5 = jgl + kbl - 1;
1571                             notrot = notrot + f2cmin(i__5,*n) - jgl + 1;
1572                         }
1573                         if (aapp < 0.f) {
1574                             notrot = 0;
1575                         }
1576
1577                     }
1578
1579 /* L2100: */
1580                 }
1581 /*     end of the p-loop */
1582 /* L2010: */
1583             }
1584 /*     end of the jbc-loop */
1585 L2011:
1586 /* 2011 bailed out of the jbc-loop */
1587 /* Computing MIN */
1588             i__4 = igl + kbl - 1;
1589             i__3 = f2cmin(i__4,*n);
1590             for (p = igl; p <= i__3; ++p) {
1591                 sva[p] = (r__1 = sva[p], abs(r__1));
1592 /* L2012: */
1593             }
1594 /* ** */
1595 /* L2000: */
1596         }
1597 /* 2000 :: end of the ibr-loop */
1598
1599         if (sva[*n] < rootbig && sva[*n] > rootsfmin) {
1600             sva[*n] = scnrm2_(m, &a[*n * a_dim1 + 1], &c__1);
1601         } else {
1602             t = 0.f;
1603             aapp = 1.f;
1604             classq_(m, &a[*n * a_dim1 + 1], &c__1, &t, &aapp);
1605             sva[*n] = t * sqrt(aapp);
1606         }
1607
1608 /*     Additional steering devices */
1609
1610         if (i__ < swband && (mxaapq <= roottol || iswrot <= *n)) {
1611             swband = i__;
1612         }
1613
1614         if (i__ > swband + 1 && mxaapq < sqrt((real) (*n)) * *tol && (real) (*
1615                 n) * mxaapq * mxsinj < *tol) {
1616             goto L1994;
1617         }
1618
1619         if (notrot >= emptsw) {
1620             goto L1994;
1621         }
1622
1623 /* L1993: */
1624     }
1625 /*     end i=1:NSWEEP loop */
1626
1627 /* #:( Reaching this point means that the procedure has not converged. */
1628     *info = *nsweep - 1;
1629     goto L1995;
1630
1631 L1994:
1632 /* #:) Reaching this point means numerical convergence after the i-th */
1633 /*     sweep. */
1634
1635     *info = 0;
1636 /* #:) INFO = 0 confirms successful iterations. */
1637 L1995:
1638
1639 /*     Sort the vector SVA() of column norms. */
1640     i__1 = *n - 1;
1641     for (p = 1; p <= i__1; ++p) {
1642         i__2 = *n - p + 1;
1643         q = isamax_(&i__2, &sva[p], &c__1) + p - 1;
1644         if (p != q) {
1645             temp1 = sva[p];
1646             sva[p] = sva[q];
1647             sva[q] = temp1;
1648             i__2 = p;
1649             aapq.r = d__[i__2].r, aapq.i = d__[i__2].i;
1650             i__2 = p;
1651             i__3 = q;
1652             d__[i__2].r = d__[i__3].r, d__[i__2].i = d__[i__3].i;
1653             i__2 = q;
1654             d__[i__2].r = aapq.r, d__[i__2].i = aapq.i;
1655             cswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1);
1656             if (rsvec) {
1657                 cswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &
1658                         c__1);
1659             }
1660         }
1661 /* L5991: */
1662     }
1663
1664     return 0;
1665 } /* cgsvj0_ */
1666