src/gromacs/linearalgebra/gmx_lapack/dsteqr.c

   1 #include <math.h>
   2 #include "gromacs/utility/real.h"
   3
   4 #include "../gmx_blas.h"
   5 #include "../gmx_lapack.h"
   6 #include "lapack_limits.h"
   7
   8 void
   9 F77_FUNC(dsteqr,DSTEQR)(const char *    compz,
  10         int *     n,
  11         double *  d__,
  12         double *  e,
  13         double *  z__,
  14         int *     ldz,
  15         double *  work,
  16         int *     info)
  17 {
  18     double c_b9 = 0.;
  19     double c_b10 = 1.;
  20     int c__0 = 0;
  21     int c__1 = 1;
  22     int c__2 = 2;
  23     int z_dim1, z_offset, i__1, i__2;
  24     double d__1, d__2;
  25
  26     double b, c__, f, g;
  27     int i__, j, k, l, m;
  28     double p, r__, s;
  29     int l1, ii, mm, lm1, mm1, nm1;
  30     double rt1, rt2, eps;
  31     int lsv;
  32     double tst, eps2;
  33     int lend, jtot;
  34     double anorm;
  35     int lendm1, lendp1;
  36     int iscale;
  37     double safmin,minval;
  38     double safmax;
  39     int lendsv;
  40     double ssfmin;
  41     int nmaxit, icompz;
  42     double ssfmax;
  43
  44
  45     --d__;
  46     --e;
  47     z_dim1 = *ldz;
  48     z_offset = 1 + z_dim1;
  49     z__ -= z_offset;
  50     --work;
  51
  52     *info = 0;
  53
  54     if (*compz=='N' || *compz=='n') {
  55         icompz = 0;
  56     } else if (*compz=='V' || *compz=='v') {
  57         icompz = 1;
  58     } else if (*compz=='I' || *compz=='i') {
  59         icompz = 2;
  60     } else {
  61         icompz = -1;
  62     }
  63     if (icompz < 0) {
  64         *info = -1;
  65     } else if (*n < 0) {
  66         *info = -2;
  67     } else if (*ldz < 1 || (icompz > 0 && *ldz < ((*n>1) ? *n : 1))) {
  68         *info = -6;
  69     }
  70     if (*info != 0) {
  71         return;
  72     }
  73
  74
  75     if (*n == 0) {
  76         return;
  77     }
  78
  79     if (*n == 1) {
  80         if (icompz == 2) {
  81             z__[z_dim1 + 1] = 1.;
  82         }
  83         return;
  84     }
  85
  86     eps = GMX_DOUBLE_EPS;
  87     d__1 = eps;
  88     eps2 = d__1 * d__1;
  89     minval = GMX_DOUBLE_MIN;
  90     safmin = minval*(1.0+GMX_DOUBLE_EPS);
  91
  92     safmax = 1. / safmin;
  93     ssfmax = sqrt(safmax) / 3.;
  94     ssfmin = sqrt(safmin) / eps2;
  95
  96     if (icompz == 2) {
  97         F77_FUNC(dlaset,DLASET)("Full", n, n, &c_b9, &c_b10, &z__[z_offset], ldz);
  98     }
  99
 100     nmaxit = *n * 30;
 101     jtot = 0;
 102
 103     l1 = 1;
 104     nm1 = *n - 1;
 105
 106 L10:
 107     if (l1 > *n) {
 108         goto L160;
 109     }
 110     if (l1 > 1) {
 111         e[l1 - 1] = 0.;
 112     }
 113     if (l1 <= nm1) {
 114         i__1 = nm1;
 115         for (m = l1; m <= i__1; ++m) {
 116             tst = fabs(e[m]);
 117             if (fabs(tst)<GMX_DOUBLE_MIN) {
 118                 goto L30;
 119             }
 120             if (tst <= sqrt(fabs(d__[m])) * sqrt(fabs(d__[m + 1])) * eps) {
 121                 e[m] = 0.;
 122                 goto L30;
 123             }
 124         }
 125     }
 126     m = *n;
 127
 128 L30:
 129     l = l1;
 130     lsv = l;
 131     lend = m;
 132     lendsv = lend;
 133     l1 = m + 1;
 134     if (lend == l) {
 135         goto L10;
 136     }
 137
 138     i__1 = lend - l + 1;
 139     anorm = F77_FUNC(dlanst,DLANST)("I", &i__1, &d__[l], &e[l]);
 140     iscale = 0;
 141     if (fabs(anorm)<GMX_DOUBLE_MIN) {
 142         goto L10;
 143     }
 144     if (anorm > ssfmax) {
 145         iscale = 1;
 146         i__1 = lend - l + 1;
 147         F77_FUNC(dlascl,DLASCL)("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n,
 148                 info);
 149         i__1 = lend - l;
 150         F77_FUNC(dlascl,DLASCL)("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n,
 151                 info);
 152     } else if (anorm < ssfmin) {
 153         iscale = 2;
 154         i__1 = lend - l + 1;
 155         F77_FUNC(dlascl,DLASCL)("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n,
 156                 info);
 157         i__1 = lend - l;
 158         F77_FUNC(dlascl,DLASCL)("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n,
 159                 info);
 160     }
 161
 162     if (fabs(d__[lend]) < fabs(d__[l])) {
 163         lend = lsv;
 164         l = lendsv;
 165     }
 166
 167     if (lend > l) {
 168
 169 L40:
 170         if (l != lend) {
 171             lendm1 = lend - 1;
 172             i__1 = lendm1;
 173             for (m = l; m <= i__1; ++m) {
 174                 d__2 = fabs(e[m]);
 175                 tst = d__2 * d__2;
 176                 if (tst <= eps2 * fabs(d__[m]) * fabs(d__[m+ 1]) + safmin) {
 177                     goto L60;
 178                 }
 179             }
 180         }
 181
 182         m = lend;
 183
 184 L60:
 185         if (m < lend) {
 186             e[m] = 0.;
 187         }
 188         p = d__[l];
 189         if (m == l) {
 190             goto L80;
 191         }
 192
 193         if (m == l + 1) {
 194             if (icompz > 0) {
 195                 F77_FUNC(dlaev2,DLAEV2)(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s);
 196                 work[l] = c__;
 197                 work[*n - 1 + l] = s;
 198                 F77_FUNC(dlasr,DLASR)("R", "V", "B", n, &c__2, &work[l], &work[*n - 1 + l], &
 199                         z__[l * z_dim1 + 1], ldz);
 200             } else {
 201                 F77_FUNC(dlae2,DLAE2)(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2);
 202             }
 203             d__[l] = rt1;
 204             d__[l + 1] = rt2;
 205             e[l] = 0.;
 206             l += 2;
 207             if (l <= lend) {
 208                 goto L40;
 209             }
 210             goto L140;
 211         }
 212
 213         if (jtot == nmaxit) {
 214             goto L140;
 215         }
 216         ++jtot;
 217
 218         g = (d__[l + 1] - p) / (e[l] * 2.);
 219         r__ = F77_FUNC(dlapy2,DLAPY2)(&g, &c_b10);
 220         g = d__[m] - p + e[l] / (g + ( (g>0) ? r__ : -r__ ) );
 221
 222         s = 1.;
 223         c__ = 1.;
 224         p = 0.;
 225
 226         mm1 = m - 1;
 227         i__1 = l;
 228         for (i__ = mm1; i__ >= i__1; --i__) {
 229             f = s * e[i__];
 230             b = c__ * e[i__];
 231             F77_FUNC(dlartg,DLARTG)(&g, &f, &c__, &s, &r__);
 232             if (i__ != m - 1) {
 233                 e[i__ + 1] = r__;
 234             }
 235             g = d__[i__ + 1] - p;
 236             r__ = (d__[i__] - g) * s + c__ * 2. * b;
 237             p = s * r__;
 238             d__[i__ + 1] = g + p;
 239             g = c__ * r__ - b;
 240
 241             if (icompz > 0) {
 242                 work[i__] = c__;
 243                 work[*n - 1 + i__] = -s;
 244             }
 245         }
 246
 247         if (icompz > 0) {
 248             mm = m - l + 1;
 249             F77_FUNC(dlasr,DLASR)("R", "V", "B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l
 250                     * z_dim1 + 1], ldz);
 251         }
 252
 253         d__[l] -= p;
 254         e[l] = g;
 255         goto L40;
 256
 257 L80:
 258         d__[l] = p;
 259
 260         ++l;
 261         if (l <= lend) {
 262             goto L40;
 263         }
 264         goto L140;
 265
 266     } else {
 267
 268 L90:
 269         if (l != lend) {
 270             lendp1 = lend + 1;
 271             i__1 = lendp1;
 272             for (m = l; m >= i__1; --m) {
 273                 d__2 = fabs(e[m - 1]);
 274                 tst = d__2 * d__2;
 275                 if (tst <= eps2 * fabs(d__[m]) * fabs(d__[m- 1]) + safmin) {
 276                     goto L110;
 277                 }
 278             }
 279         }
 280
 281         m = lend;
 282
 283 L110:
 284         if (m > lend) {
 285             e[m - 1] = 0.;
 286         }
 287         p = d__[l];
 288         if (m == l) {
 289             goto L130;
 290         }
 291         if (m == l - 1) {
 292             if (icompz > 0) {
 293                 F77_FUNC(dlaev2,DLAEV2)(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s)
 294                         ;
 295                 work[m] = c__;
 296                 work[*n - 1 + m] = s;
 297                 F77_FUNC(dlasr,DLASR)("R", "V", "F", n, &c__2, &work[m], &work[*n - 1 + m], &
 298                         z__[(l - 1) * z_dim1 + 1], ldz);
 299             } else {
 300                 F77_FUNC(dlae2,DLAE2)(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2);
 301             }
 302             d__[l - 1] = rt1;
 303             d__[l] = rt2;
 304             e[l - 1] = 0.;
 305             l += -2;
 306             if (l >= lend) {
 307                 goto L90;
 308             }
 309             goto L140;
 310         }
 311
 312         if (jtot == nmaxit) {
 313             goto L140;
 314         }
 315         ++jtot;
 316
 317         g = (d__[l - 1] - p) / (e[l - 1] * 2.);
 318         r__ = F77_FUNC(dlapy2,DLAPY2)(&g, &c_b10);
 319         g = d__[m] - p + e[l - 1] / (g + ( (g>0) ? r__ : -r__ ));
 320
 321         s = 1.;
 322         c__ = 1.;
 323         p = 0.;
 324
 325         lm1 = l - 1;
 326         i__1 = lm1;
 327         for (i__ = m; i__ <= i__1; ++i__) {
 328             f = s * e[i__];
 329             b = c__ * e[i__];
 330             F77_FUNC(dlartg,DLARTG)(&g, &f, &c__, &s, &r__);
 331             if (i__ != m) {
 332                 e[i__ - 1] = r__;
 333             }
 334             g = d__[i__] - p;
 335             r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b;
 336             p = s * r__;
 337             d__[i__] = g + p;
 338             g = c__ * r__ - b;
 339
 340             if (icompz > 0) {
 341                 work[i__] = c__;
 342                 work[*n - 1 + i__] = s;
 343             }
 344         }
 345
 346         if (icompz > 0) {
 347             mm = l - m + 1;
 348             F77_FUNC(dlasr,DLASR)("R", "V", "F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m
 349                     * z_dim1 + 1], ldz);
 350         }
 351
 352         d__[l] -= p;
 353         e[lm1] = g;
 354         goto L90;
 355
 356 L130:
 357         d__[l] = p;
 358
 359         --l;
 360         if (l >= lend) {
 361             goto L90;
 362         }
 363         goto L140;
 364
 365     }
 366
 367 L140:
 368     if (iscale == 1) {
 369         i__1 = lendsv - lsv + 1;
 370         F77_FUNC(dlascl,DLASCL)("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv],
 371                 n, info);
 372         i__1 = lendsv - lsv;
 373         F77_FUNC(dlascl,DLASCL)("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n,
 374                 info);
 375     } else if (iscale == 2) {
 376         i__1 = lendsv - lsv + 1;
 377         F77_FUNC(dlascl,DLASCL)("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv],
 378                 n, info);
 379         i__1 = lendsv - lsv;
 380         F77_FUNC(dlascl,DLASCL)("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n,
 381                 info);
 382     }
 383
 384     if (jtot < nmaxit) {
 385         goto L10;
 386     }
 387     i__1 = *n - 1;
 388     for (i__ = 1; i__ <= i__1; ++i__) {
 389         if (fabs(e[i__])>GMX_DOUBLE_MIN) {
 390             ++(*info);
 391         }
 392     }
 393     goto L190;
 394
 395 L160:
 396     if (icompz == 0) {
 397
 398         F77_FUNC(dlasrt,DLASRT)("I", n, &d__[1], info);
 399
 400     } else {
 401
 402         i__1 = *n;
 403         for (ii = 2; ii <= i__1; ++ii) {
 404             i__ = ii - 1;
 405             k = i__;
 406             p = d__[i__];
 407             i__2 = *n;
 408             for (j = ii; j <= i__2; ++j) {
 409                 if (d__[j] < p) {
 410                     k = j;
 411                     p = d__[j];
 412                 }
 413             }
 414             if (k != i__) {
 415                 d__[k] = d__[i__];
 416                 d__[i__] = p;
 417                 F77_FUNC(dswap,DSWAP)(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1],
 418                          &c__1);
 419             }
 420         }
 421     }
 422
 423 L190:
 424     return;
 425 }
 426
 427