Date: 2016-07-24T17:06:17+00:00

Actual source code: cgeig.c
petsc-3.7.3 2016-07-24
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      2: /*
      3:       Code for calculating extreme eigenvalues via the Lanczo method
      4:    running with CG. Note this only works for symmetric real and Hermitian
      5:    matrices (not complex matrices that are symmetric).
      6: */
      7: #include <../src/ksp/ksp/impls/cg/cgimpl.h>
      8: static PetscErrorCode LINPACKcgtql1(PetscInt*,PetscReal*,PetscReal*,PetscInt*);

     12: PetscErrorCode KSPComputeEigenvalues_CG(KSP ksp,PetscInt nmax,PetscReal *r,PetscReal *c,PetscInt *neig)
     13: {
     14:   KSP_CG         *cgP = (KSP_CG*)ksp->data;
     15:   PetscScalar    *d,*e;
     16:   PetscReal      *ee;
     18:   PetscInt       j,n = cgP->ned;

     21:   if (nmax < n) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_SIZ,"Not enough room in work space r and c for eigenvalues");
     22:   *neig = n;

     24:   PetscMemzero(c,nmax*sizeof(PetscReal));
     25:   if (!n) {
     26:     return(0);
     27:   }
     28:   d = cgP->d; e = cgP->e; ee = cgP->ee;

     30:   /* copy tridiagonal matrix to work space */
     31:   for (j=0; j<n; j++) {
     32:     r[j]  = PetscRealPart(d[j]);
     33:     ee[j] = PetscRealPart(e[j]);
     34:   }

     36:   LINPACKcgtql1(&n,r,ee,&j);
     37:   if (j != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error from tql1(); eispack eigenvalue routine");
     38:   PetscSortReal(n,r);
     39:   return(0);
     40: }

     44: PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP ksp,PetscReal *emax,PetscReal *emin)
     45: {
     46:   KSP_CG      *cgP = (KSP_CG*)ksp->data;
     47:   PetscScalar *d,*e;
     48:   PetscReal   *dd,*ee;
     49:   PetscInt    j,n = cgP->ned;

     52:   if (!n) {
     53:     *emax = *emin = 1.0;
     54:     return(0);
     55:   }
     56:   d = cgP->d; e = cgP->e; dd = cgP->dd; ee = cgP->ee;

     58:   /* copy tridiagonal matrix to work space */
     59:   for (j=0; j<n; j++) {
     60:     dd[j] = PetscRealPart(d[j]);
     61:     ee[j] = PetscRealPart(e[j]);
     62:   }

     64:   LINPACKcgtql1(&n,dd,ee,&j);
     65:   if (j != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error from tql1(); eispack eigenvalue routine");
     66:   *emin = dd[0]; *emax = dd[n-1];
     67:   return(0);
     68: }

     70: /* tql1.f -- translated by f2c (version of 25 March 1992  12:58:56).
     71:    By Barry Smith on March 27, 1994.
     72:    Eispack routine to determine eigenvalues of symmetric
     73:    tridiagonal matrix

     75:   Note that this routine always uses real numbers (not complex) even if the underlying
     76:   matrix is Hermitian. This is because the Lanczos process applied to Hermitian matrices
     77:   always produces a real, symmetric tridiagonal matrix.
     78: */

     80: static PetscReal LINPACKcgpthy(PetscReal*,PetscReal*);

     84: static PetscErrorCode LINPACKcgtql1(PetscInt *n,PetscReal *d,PetscReal *e,PetscInt *ierr)
     85: {
     86:   /* System generated locals */
     87:   PetscInt  i__1,i__2;
     88:   PetscReal d__1,d__2,c_b10 = 1.0;

     90:   /* Local variables */
     91:   PetscReal c,f,g,h;
     92:   PetscInt  i,j,l,m;
     93:   PetscReal p,r,s,c2,c3 = 0.0;
     94:   PetscInt  l1,l2;
     95:   PetscReal s2 = 0.0;
     96:   PetscInt  ii;
     97:   PetscReal dl1,el1;
     98:   PetscInt  mml;
     99:   PetscReal tst1,tst2;

    101: /*     THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE TQL1, */
    102: /*     NUM. MATH. 11, 293-306(1968) BY BOWDLER, MARTIN, REINSCH, AND */
    103: /*     WILKINSON. */
    104: /*     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 227-240(1971). */

    106: /*     THIS SUBROUTINE FINDS THE EIGENVALUES OF A SYMMETRIC */
    107: /*     TRIDIAGONAL MATRIX BY THE QL METHOD. */

    109: /*     ON INPUT */

    111: /*        N IS THE ORDER OF THE MATRIX. */

    113: /*        D CONTAINS THE DIAGONAL ELEMENTS OF THE INPUT MATRIX. */

    115: /*        E CONTAINS THE SUBDIAGONAL ELEMENTS OF THE INPUT MATRIX */
    116: /*          IN ITS LAST N-1 POSITIONS.  E(1) IS ARBITRARY. */

    118: /*      ON OUTPUT */

    120: /*        D CONTAINS THE EIGENVALUES IN ASCENDING ORDER.  IF AN */
    121: /*          ERROR EXIT IS MADE, THE EIGENVALUES ARE CORRECT AND */
    122: /*          ORDERED FOR INDICES 1,2,...IERR-1, BUT MAY NOT BE */
    123: /*          THE SMALLEST EIGENVALUES. */

    125: /*        E HAS BEEN DESTROYED. */

    127: /*        IERR IS SET TO */
    128: /*          ZERO       FOR NORMAL RETURN, */
    129: /*          J          IF THE J-TH EIGENVALUE HAS NOT BEEN */
    130: /*                     DETERMINED AFTER 30 ITERATIONS. */

    132: /*     CALLS CGPTHY FOR  DSQRT(A*A + B*B) . */

    134: /*     QUESTIONS AND COMMENTS SHOULD BE DIRECTED TO BURTON S. GARBOW, */
    135: /*     MATHEMATICS AND COMPUTER SCIENCE DIV, ARGONNE NATIONAL LABORATORY
    136: */

    138: /*     THIS VERSION DATED AUGUST 1983. */

    140: /*     ------------------------------------------------------------------
    141: */
    142:   PetscReal ds;

    145:   --e;
    146:   --d;

    148:   *0;
    149:   if (*n == 1) goto L1001;

    152:   i__1 = *n;
    153:   for (i = 2; i <= i__1; ++i) e[i - 1] = e[i];

    155:   f     = 0.;
    156:   tst1  = 0.;
    157:   e[*n] = 0.;

    159:   i__1 = *n;
    160:   for (l = 1; l <= i__1; ++l) {
    161:     j = 0;
    162:     h = (d__1 = d[l],PetscAbsReal(d__1)) + (d__2 = e[l],PetscAbsReal(d__2));
    163:     if (tst1 < h) tst1 = h;
    164: /*     .......... LOOK FOR SMALL SUB-DIAGONAL ELEMENT .......... */
    165:     i__2 = *n;
    166:     for (m = l; m <= i__2; ++m) {
    167:       tst2 = tst1 + (d__1 = e[m],PetscAbsReal(d__1));
    168:       if (tst2 == tst1) goto L120;
    169: /*     .......... E(N) IS ALWAYS ZERO,SO THERE IS NO EXIT */
    170: /*                THROUGH THE BOTTOM OF THE LOOP .......... */
    171:     }
    172: L120:
    173:     if (m == l) goto L210;
    174: L130:
    175:     if (j == 30) goto L1000;
    176:     ++j;
    177: /*     .......... FORM SHIFT .......... */
    178:     l1    = l + 1;
    179:     l2    = l1 + 1;
    180:     g     = d[l];
    181:     p     = (d[l1] - g) / (e[l] * 2.);
    182:     r     = LINPACKcgpthy(&p,&c_b10);
    183:     ds    = 1.0; if (p < 0.0) ds = -1.0;
    184:     d[l]  = e[l] / (p + ds*r);
    185:     d[l1] = e[l] * (p + ds*r);
    186:     dl1   = d[l1];
    187:     h     = g - d[l];
    188:     if (l2 > *n) goto L145;

    190:     i__2 = *n;
    191:     for (i = l2; i <= i__2; ++i) d[i] -= h;

    193: L145:
    194:     f += h;
    195: /*     .......... QL TRANSFORMATION .......... */
    196:     p   = d[m];
    197:     c   = 1.;
    198:     c2  = c;
    199:     el1 = e[l1];
    200:     s   = 0.;
    201:     mml = m - l;
    202: /*     .......... FOR I=M-1 STEP -1 UNTIL L DO -- .......... */
    203:     i__2 = mml;
    204:     for (ii = 1; ii <= i__2; ++ii) {
    205:       c3       = c2;
    206:       c2       = c;
    207:       s2       = s;
    208:       i        = m - ii;
    209:       g        = c * e[i];
    210:       h        = c * p;
    211:       r        = LINPACKcgpthy(&p,&e[i]);
    212:       e[i + 1] = s * r;
    213:       s        = e[i] / r;
    214:       c        = p / r;
    215:       p        = c * d[i] - s * g;
    216:       d[i + 1] = h + s * (c * g + s * d[i]);
    217:     }

    219:     p    = -s * s2 * c3 * el1 * e[l] / dl1;
    220:     e[l] = s * p;
    221:     d[l] = c * p;
    222:     tst2 = tst1 + (d__1 = e[l],PetscAbsReal(d__1));
    223:     if (tst2 > tst1) goto L130;
    224: L210:
    225:     p = d[l] + f;
    226: /*     .......... ORDER EIGENVALUES .......... */
    227:     if (l == 1) goto L250;
    228: /*     .......... FOR I=L STEP -1 UNTIL 2 DO -- .......... */
    229:     i__2 = l;
    230:     for (ii = 2; ii <= i__2; ++ii) {
    231:       i = l + 2 - ii;
    232:       if (p >= d[i - 1]) goto L270;
    233:       d[i] = d[i - 1];
    234:     }

    236: L250:
    237:     i = 1;
    238: L270:
    239:     d[i] = p;
    240:   }

    242:   goto L1001;
    243: /*     .......... SET ERROR -- NO CONVERGENCE TO AN */
    244: /*                EIGENVALUE AFTER 30 ITERATIONS .......... */
    245: L1000:
    246:   *l;
    247: L1001:
    248:   return(0);
    249: } /* cgtql1_ */

    253: static PetscReal LINPACKcgpthy(PetscReal *a,PetscReal *b)
    254: {
    255:   /* System generated locals */
    256:   PetscReal ret_val,d__1,d__2,d__3;

    258:   /* Local variables */
    259:   PetscReal p,r,s,t,u;

    262: /*     FINDS DSQRT(A**2+B**2) WITHOUT OVERFLOW OR DESTRUCTIVE UNDERFLOW */

    265: /* Computing MAX */
    266:   d__1 = PetscAbsReal(*a),d__2 = PetscAbsReal(*b);
    267:   p    = PetscMax(d__1,d__2);
    268:   if (!p) goto L20;
    269: /* Computing MIN */
    270:   d__2 = PetscAbsReal(*a),d__3 = PetscAbsReal(*b);
    271: /* Computing 2nd power */
    272:   d__1 = PetscMin(d__2,d__3) / p;
    273:   r    = d__1 * d__1;
    274: L10:
    275:   t = r + 4.;
    276:   if (t == 4.) goto L20;
    277:   s = r / t;
    278:   u = s * 2. + 1.;
    279:   p = u * p;
    280: /* Computing 2nd power */
    281:   d__1 = s / u;
    282:   r    = d__1 * d__1 * r;
    283:   goto L10;
    284: L20:
    285:   ret_val = p;
    286:   PetscFunctionReturn(ret_val);
    287: } /* cgpthy_ */