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>
9: /* tql1.f -- translated by f2c (version of 25 March 1992 12:58:56).
10: By Barry Smith on March 27, 1994.
11: Eispack routine to determine eigenvalues of symmetric
12: tridiagonal matrix
14: Note that this routine always uses real numbers (not complex) even if the underlying
15: matrix is Hermitian. This is because the Lanczos process applied to Hermitian matrices
16: always produces a real, symmetric tridiagonal matrix.
17: */
19: static PetscReal LINPACKcgpthy(PetscReal *a, PetscReal *b)
20: {
21: /* System generated locals */
22: PetscReal d__1, d__2, d__3;
24: /* Local variables */
25: PetscReal p, r, s, t, u;
27: /* FINDS DSQRT(A**2+B**2) WITHOUT OVERFLOW OR DESTRUCTIVE UNDERFLOW */
29: /* Computing MAX */
30: d__1 = PetscAbsReal(*a);
31: d__2 = PetscAbsReal(*b);
32: p = PetscMax(d__1, d__2);
33: if (!p) goto L20;
34: /* Computing MIN */
35: d__2 = PetscAbsReal(*a);
36: d__3 = PetscAbsReal(*b);
37: /* Computing 2nd power */
38: d__1 = PetscMin(d__2, d__3) / p;
39: r = d__1 * d__1;
40: L10:
41: t = r + 4.;
42: if (t == 4.) goto L20;
43: s = r / t;
44: u = s * 2. + 1.;
45: p = u * p;
46: /* Computing 2nd power */
47: d__1 = s / u;
48: r = d__1 * d__1 * r;
49: goto L10;
50: L20:
51: return p;
52: } /* cgpthy_ */
54: static PetscErrorCode LINPACKcgtql1(PetscInt *n, PetscReal *d, PetscReal *e, PetscInt *ierr)
55: {
56: /* System generated locals */
57: PetscInt i__1, i__2;
58: PetscReal d__1, d__2, c_b10 = 1.0;
60: /* Local variables */
61: PetscReal c, f, g, h;
62: PetscInt i, j, l, m;
63: PetscReal p, r, s, c2, c3 = 0.0;
64: PetscInt l1, l2;
65: PetscReal s2 = 0.0;
66: PetscInt ii;
67: PetscReal dl1, el1;
68: PetscInt mml;
69: PetscReal tst1, tst2;
71: /* THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE TQL1, */
72: /* NUM. MATH. 11, 293-306(1968) BY BOWDLER, MARTIN, REINSCH, AND */
73: /* WILKINSON. */
74: /* HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 227-240(1971). */
76: /* THIS SUBROUTINE FINDS THE EIGENVALUES OF A SYMMETRIC */
77: /* TRIDIAGONAL MATRIX BY THE QL METHOD. */
79: /* ON INPUT */
81: /* N IS THE ORDER OF THE MATRIX. */
83: /* D CONTAINS THE DIAGONAL ELEMENTS OF THE INPUT MATRIX. */
85: /* E CONTAINS THE SUBDIAGONAL ELEMENTS OF THE INPUT MATRIX */
86: /* IN ITS LAST N-1 POSITIONS. E(1) IS ARBITRARY. */
88: /* ON OUTPUT */
90: /* D CONTAINS THE EIGENVALUES IN ASCENDING ORDER. IF AN */
91: /* ERROR EXIT IS MADE, THE EIGENVALUES ARE CORRECT AND */
92: /* ORDERED FOR INDICES 1,2,...IERR-1, BUT MAY NOT BE */
93: /* THE SMALLEST EIGENVALUES. */
95: /* E HAS BEEN DESTROYED. */
97: /* IERR IS SET TO */
98: /* ZERO FOR NORMAL RETURN, */
99: /* J IF THE J-TH EIGENVALUE HAS NOT BEEN */
100: /* DETERMINED AFTER 30 ITERATIONS. */
102: /* CALLS CGPTHY FOR DSQRT(A*A + B*B) . */
104: /* QUESTIONS AND COMMENTS SHOULD BE DIRECTED TO BURTON S. GARBOW, */
105: /* MATHEMATICS AND COMPUTER SCIENCE DIV, ARGONNE NATIONAL LABORATORY
106: */
108: /* THIS VERSION DATED AUGUST 1983. */
110: /* ------------------------------------------------------------------
111: */
112: PetscReal ds;
114: --e;
115: --d;
117: *0;
118: if (*n == 1) goto L1001;
120: i__1 = *n;
121: for (i = 2; i <= i__1; ++i) e[i - 1] = e[i];
123: f = 0.;
124: tst1 = 0.;
125: e[*n] = 0.;
127: i__1 = *n;
128: for (l = 1; l <= i__1; ++l) {
129: j = 0;
130: d__1 = d[l];
131: d__2 = e[l];
132: h = PetscAbsReal(d__1) + PetscAbsReal(d__2);
133: if (tst1 < h) tst1 = h;
134: /* .......... LOOK FOR SMALL SUB-DIAGONAL ELEMENT .......... */
135: i__2 = *n;
136: for (m = l; m <= i__2; ++m) {
137: d__1 = e[m];
138: tst2 = tst1 + PetscAbsReal(d__1);
139: if (tst2 == tst1) goto L120;
140: /* .......... E(N) IS ALWAYS ZERO,SO THERE IS NO EXIT */
141: /* THROUGH THE BOTTOM OF THE LOOP .......... */
142: }
143: L120:
144: if (m == l) goto L210;
145: L130:
146: if (j == 30) goto L1000;
147: ++j;
148: /* .......... FORM SHIFT .......... */
149: l1 = l + 1;
150: l2 = l1 + 1;
151: g = d[l];
152: p = (d[l1] - g) / (e[l] * 2.);
153: r = LINPACKcgpthy(&p, &c_b10);
154: ds = 1.0;
155: if (p < 0.0) ds = -1.0;
156: d[l] = e[l] / (p + ds * r);
157: d[l1] = e[l] * (p + ds * r);
158: dl1 = d[l1];
159: h = g - d[l];
160: if (l2 > *n) goto L145;
162: i__2 = *n;
163: for (i = l2; i <= i__2; ++i) d[i] -= h;
165: L145:
166: f += h;
167: /* .......... QL TRANSFORMATION .......... */
168: p = d[m];
169: c = 1.;
170: c2 = c;
171: el1 = e[l1];
172: s = 0.;
173: mml = m - l;
174: /* .......... FOR I=M-1 STEP -1 UNTIL L DO -- .......... */
175: i__2 = mml;
176: for (ii = 1; ii <= i__2; ++ii) {
177: c3 = c2;
178: c2 = c;
179: s2 = s;
180: i = m - ii;
181: g = c * e[i];
182: h = c * p;
183: r = LINPACKcgpthy(&p, &e[i]);
184: e[i + 1] = s * r;
185: s = e[i] / r;
186: c = p / r;
187: p = c * d[i] - s * g;
188: d[i + 1] = h + s * (c * g + s * d[i]);
189: }
191: p = -s * s2 * c3 * el1 * e[l] / dl1;
192: e[l] = s * p;
193: d[l] = c * p;
194: d__1 = e[l];
195: tst2 = tst1 + PetscAbsReal(d__1);
196: if (tst2 > tst1) goto L130;
197: L210:
198: p = d[l] + f;
199: /* .......... ORDER EIGENVALUES .......... */
200: if (l == 1) goto L250;
201: /* .......... FOR I=L STEP -1 UNTIL 2 DO -- .......... */
202: i__2 = l;
203: for (ii = 2; ii <= i__2; ++ii) {
204: i = l + 2 - ii;
205: if (p >= d[i - 1]) goto L270;
206: d[i] = d[i - 1];
207: }
209: L250:
210: i = 1;
211: L270:
212: d[i] = p;
213: }
215: goto L1001;
216: /* .......... SET ERROR -- NO CONVERGENCE TO AN */
217: /* EIGENVALUE AFTER 30 ITERATIONS .......... */
218: L1000:
219: *l;
220: L1001:
221: return 0;
222: } /* cgtql1_ */
224: PetscErrorCode KSPComputeEigenvalues_CG(KSP ksp, PetscInt nmax, PetscReal *r, PetscReal *c, PetscInt *neig)
225: {
226: KSP_CG *cgP = (KSP_CG *)ksp->data;
227: PetscScalar *d, *e;
228: PetscReal *ee;
229: PetscInt j, n = ksp->its;
232: *neig = n;
234: PetscArrayzero(c, nmax);
235: if (!n) return 0;
236: d = cgP->d;
237: e = cgP->e;
238: ee = cgP->ee;
240: /* copy tridiagonal matrix to work space */
241: for (j = 0; j < n; j++) {
242: r[j] = PetscRealPart(d[j]);
243: ee[j] = PetscRealPart(e[j]);
244: }
246: LINPACKcgtql1(&n, r, ee, &j);
248: PetscSortReal(n, r);
249: return 0;
250: }
252: PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP ksp, PetscReal *emax, PetscReal *emin)
253: {
254: KSP_CG *cgP = (KSP_CG *)ksp->data;
255: PetscScalar *d, *e;
256: PetscReal *dd, *ee;
257: PetscInt j, n = ksp->its;
259: if (!n) {
260: *emax = *emin = 1.0;
261: return 0;
262: }
263: d = cgP->d;
264: e = cgP->e;
265: dd = cgP->dd;
266: ee = cgP->ee;
268: /* copy tridiagonal matrix to work space */
269: for (j = 0; j < n; j++) {
270: dd[j] = PetscRealPart(d[j]);
271: ee[j] = PetscRealPart(e[j]);
272: }
274: LINPACKcgtql1(&n, dd, ee, &j);
276: *emin = dd[0];
277: *emax = dd[n - 1];
278: return 0;
279: }