Actual source code: cgeig.c


  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*);

 10: PetscErrorCode KSPComputeEigenvalues_CG(KSP ksp,PetscInt nmax,PetscReal *r,PetscReal *c,PetscInt *neig)
 11: {
 12:   KSP_CG         *cgP = (KSP_CG*)ksp->data;
 13:   PetscScalar    *d,*e;
 14:   PetscReal      *ee;
 16:   PetscInt       j,n = cgP->ned;

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

 22:   PetscArrayzero(c,nmax);
 23:   if (!n) {
 24:     return(0);
 25:   }
 26:   d = cgP->d; e = cgP->e; ee = cgP->ee;

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

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

 40: PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP ksp,PetscReal *emax,PetscReal *emin)
 41: {
 42:   KSP_CG      *cgP = (KSP_CG*)ksp->data;
 43:   PetscScalar *d,*e;
 44:   PetscReal   *dd,*ee;
 45:   PetscInt    j,n = cgP->ned;

 48:   if (!n) {
 49:     *emax = *emin = 1.0;
 50:     return(0);
 51:   }
 52:   d = cgP->d; e = cgP->e; dd = cgP->dd; ee = cgP->ee;

 54:   /* copy tridiagonal matrix to work space */
 55:   for (j=0; j<n; j++) {
 56:     dd[j] = PetscRealPart(d[j]);
 57:     ee[j] = PetscRealPart(e[j]);
 58:   }

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

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

 71:   Note that this routine always uses real numbers (not complex) even if the underlying
 72:   matrix is Hermitian. This is because the Lanczos process applied to Hermitian matrices
 73:   always produces a real, symmetric tridiagonal matrix.
 74: */

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

 78: static PetscErrorCode LINPACKcgtql1(PetscInt *n,PetscReal *d,PetscReal *e,PetscInt *ierr)
 79: {
 80:   /* System generated locals */
 81:   PetscInt  i__1,i__2;
 82:   PetscReal d__1,d__2,c_b10 = 1.0;

 84:   /* Local variables */
 85:   PetscReal c,f,g,h;
 86:   PetscInt  i,j,l,m;
 87:   PetscReal p,r,s,c2,c3 = 0.0;
 88:   PetscInt  l1,l2;
 89:   PetscReal s2 = 0.0;
 90:   PetscInt  ii;
 91:   PetscReal dl1,el1;
 92:   PetscInt  mml;
 93:   PetscReal tst1,tst2;

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

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

103: /*     ON INPUT */

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

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

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

112: /*      ON OUTPUT */

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

119: /*        E HAS BEEN DESTROYED. */

121: /*        IERR IS SET TO */
122: /*          ZERO       FOR NORMAL RETURN, */
123: /*          J          IF THE J-TH EIGENVALUE HAS NOT BEEN */
124: /*                     DETERMINED AFTER 30 ITERATIONS. */

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

128: /*     QUESTIONS AND COMMENTS SHOULD BE DIRECTED TO BURTON S. GARBOW, */
129: /*     MATHEMATICS AND COMPUTER SCIENCE DIV, ARGONNE NATIONAL LABORATORY
130: */

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

134: /*     ------------------------------------------------------------------
135: */
136:   PetscReal ds;

139:   --e;
140:   --d;

142:   *0;
143:   if (*n == 1) goto L1001;

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

148:   f     = 0.;
149:   tst1  = 0.;
150:   e[*n] = 0.;

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

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

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

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

233: L250:
234:     i = 1;
235: L270:
236:     d[i] = p;
237:   }

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

248: static PetscReal LINPACKcgpthy(PetscReal *a,PetscReal *b)
249: {
250:   /* System generated locals */
251:   PetscReal ret_val,d__1,d__2,d__3;

253:   /* Local variables */
254:   PetscReal p,r,s,t,u;

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

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