1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
10: /*
11: BDC - Block-divide and conquer (see description in README file)
12: */
14: #include <slepc/private/dsimpl.h> 15: #include <slepcblaslapack.h> 17: PetscErrorCode BDC_dlaed3m_(const char *jobz,const char *defl,PetscBLASInt k,PetscBLASInt n, 18: PetscBLASInt n1,PetscReal *d,PetscReal *q,PetscBLASInt ldq, 19: PetscReal rho,PetscReal *dlamda,PetscReal *q2,PetscBLASInt *indx, 20: PetscBLASInt *ctot,PetscReal *w,PetscReal *s,PetscBLASInt *info, 21: PetscBLASInt jobz_len,PetscBLASInt defl_len) 22: {
23: /* -- Routine written in LAPACK version 3.0 style -- */
24: /* *************************************************** */
25: /* Written by */
26: /* Michael Moldaschl and Wilfried Gansterer */
27: /* University of Vienna */
28: /* last modification: March 16, 2014 */
30: /* Small adaptations of original code written by */
31: /* Wilfried Gansterer and Bob Ward, */
32: /* Department of Computer Science, University of Tennessee */
33: /* see https://doi.org/10.1137/S1064827501399432 */
34: /* *************************************************** */
36: /* Purpose */
37: /* ======= */
39: /* DLAED3M finds the roots of the secular equation, as defined by the */
40: /* values in D, W, and RHO, between 1 and K. It makes the */
41: /* appropriate calls to DLAED4 and then updates the eigenvectors by */
42: /* multiplying the matrix of eigenvectors of the pair of eigensystems */
43: /* being combined by the matrix of eigenvectors of the K-by-K system */
44: /* which is solved here. */
46: /* This code makes very mild assumptions about floating point */
47: /* arithmetic. It will work on machines with a guard digit in */
48: /* add/subtract, or on those binary machines without guard digits */
49: /* which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
50: /* It could conceivably fail on hexadecimal or decimal machines */
51: /* without guard digits, but we know of none. */
53: /* Arguments */
54: /* ========= */
56: /* JOBZ (input) CHARACTER*1 */
57: /* = 'N': Do not accumulate eigenvectors (not implemented); */
58: /* = 'D': Do accumulate eigenvectors in the divide-and-conquer */
59: /* process. */
61: /* DEFL (input) CHARACTER*1 */
62: /* = '0': No deflation happened in DSRTDF */
63: /* = '1': Some deflation happened in DSRTDF (and therefore some */
64: /* Givens rotations need to be applied to the computed */
65: /* eigenvector matrix Q) */
67: /* K (input) INTEGER */
68: /* The number of terms in the rational function to be solved by */
69: /* DLAED4. 0 <= K <= N. */
71: /* N (input) INTEGER */
72: /* The number of rows and columns in the Q matrix. */
73: /* N >= K (deflation may result in N>K). */
75: /* N1 (input) INTEGER */
76: /* The location of the last eigenvalue in the leading submatrix. */
77: /* min(1,N) <= N1 <= max(1,N-1). */
79: /* D (output) DOUBLE PRECISION array, dimension (N) */
80: /* D(I) contains the updated eigenvalues for */
81: /* 1 <= I <= K. */
83: /* Q (output) DOUBLE PRECISION array, dimension (LDQ,N) */
84: /* Initially the first K columns are used as workspace. */
85: /* On output the columns 1 to K contain */
86: /* the updated eigenvectors. */
88: /* LDQ (input) INTEGER */
89: /* The leading dimension of the array Q. LDQ >= max(1,N). */
91: /* RHO (input) DOUBLE PRECISION */
92: /* The value of the parameter in the rank one update equation. */
93: /* RHO >= 0 required. */
95: /* DLAMDA (input/output) DOUBLE PRECISION array, dimension (K) */
96: /* The first K elements of this array contain the old roots */
97: /* of the deflated updating problem. These are the poles */
98: /* of the secular equation. May be changed on output by */
99: /* having lowest order bit set to zero on Cray X-MP, Cray Y-MP, */
100: /* Cray-2, or Cray C-90, as described above. */
102: /* Q2 (input) DOUBLE PRECISION array, dimension (LDQ2, N) */
103: /* The first K columns of this matrix contain the non-deflated */
104: /* eigenvectors for the split problem. */
106: /* INDX (input) INTEGER array, dimension (N) */
107: /* The permutation used to arrange the columns of the deflated */
108: /* Q matrix into three groups (see DLAED2). */
109: /* The rows of the eigenvectors found by DLAED4 must be likewise */
110: /* permuted before the matrix multiply can take place. */
112: /* CTOT (input) INTEGER array, dimension (4) */
113: /* A count of the total number of the various types of columns */
114: /* in Q, as described in INDX. The fourth column type is any */
115: /* column which has been deflated. */
117: /* W (input/output) DOUBLE PRECISION array, dimension (K) */
118: /* The first K elements of this array contain the components */
119: /* of the deflation-adjusted updating vector. Destroyed on */
120: /* output. */
122: /* S (workspace) DOUBLE PRECISION array, dimension */
123: /* (MAX(CTOT(1)+CTOT(2),CTOT(2)+CTOT(3)) + 1)*K */
124: /* Will contain parts of the eigenvectors of the repaired matrix */
125: /* which will be multiplied by the previously accumulated */
126: /* eigenvectors to update the system. This array is a major */
127: /* source of workspace requirements ! */
129: /* INFO (output) INTEGER */
130: /* = 0: successful exit. */
131: /* < 0: if INFO = -i, the i-th argument had an illegal value. */
132: /* > 0: if INFO = i, eigenpair i was not computed successfully */
134: /* Further Details */
135: /* =============== */
137: /* Based on code written by */
138: /* Wilfried Gansterer and Bob Ward, */
139: /* Department of Computer Science, University of Tennessee */
140: /* Based on the design of the LAPACK code DLAED3 with small modifications */
141: /* (Note that in contrast to the original DLAED3, this routine */
142: /* DOES NOT require that N1 <= N/2) */
144: /* Based on contributions by */
145: /* Jeff Rutter, Computer Science Division, University of California */
146: /* at Berkeley, USA */
147: /* Modified by Francoise Tisseur, University of Tennessee. */
149: /* ===================================================================== */
151: PetscReal temp, done = 1.0, dzero = 0.0;
152: PetscBLASInt i, j, n2, n12, ii, n23, iq2, i1, one=1;
154: PetscFunctionBegin;
155: *info = 0;
157: if (k < 0) *info = -3;
158: else if (n < k) *info = -4;
159: else if (n1 < PetscMin(1,n) || n1 > PetscMax(1,n)) *info = -5;
160: else if (ldq < PetscMax(1,n)) *info = -8;
161: else if (rho < 0.) *info = -9;
162: PetscCheck(!*info,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong argument %" PetscBLASInt_FMT " in DLAED3M",-(*info));
164: /* Quick return if possible */
166: if (k == 0) PetscFunctionReturn(PETSC_SUCCESS);
168: /* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */
169: /* be computed with high relative accuracy (barring over/underflow). */
170: /* This is a problem on machines without a guard digit in */
171: /* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */
172: /* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */
173: /* which on any of these machines zeros out the bottommost */
174: /* bit of DLAMDA(I) if it is 1; this makes the subsequent */
175: /* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */
176: /* occurs. On binary machines with a guard digit (almost all */
177: /* machines) it does not change DLAMDA(I) at all. On hexadecimal */
178: /* and decimal machines with a guard digit, it slightly */
179: /* changes the bottommost bits of DLAMDA(I). It does not account */
180: /* for hexadecimal or decimal machines without guard digits */
181: /* (we know of none). We use a subroutine call to compute */
182: /* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */
183: /* this code. */
185: for (i = 0; i < k; ++i) {
186: dlamda[i] = LAPACKlamc3_(&dlamda[i], &dlamda[i]) - dlamda[i];
187: }
189: for (j = 1; j <= k; ++j) {
191: /* ....calling DLAED4 for eigenpair J.... */
193: PetscCallBLAS("LAPACKlaed4",LAPACKlaed4_(&k, &j, dlamda, w, &q[(j-1)*ldq], &rho, &d[j-1], info));
194: SlepcCheckLapackInfo("laed4",*info);
196: if (j < k) {
198: /* If the zero finder terminated properly, but the computed */
199: /* eigenvalues are not ordered, issue an error statement */
200: /* but continue computation. */
202: PetscCheck(dlamda[j-1]<dlamda[j],PETSC_COMM_SELF,PETSC_ERR_FP,"DLAMDA(%" PetscBLASInt_FMT ") is greater or equal than DLAMDA(%" PetscBLASInt_FMT ")", j, j+1);
203: PetscCheck(d[j-1]>=dlamda[j-1] && d[j-1]<=dlamda[j],PETSC_COMM_SELF,PETSC_ERR_FP,"DLAMDA(%" PetscBLASInt_FMT ") = %g D(%" PetscBLASInt_FMT ") = %g DLAMDA(%" PetscBLASInt_FMT ") = %g", j, (double)dlamda[j-1], j, (double)d[j-1], j+1, (double)dlamda[j]);
204: }
205: }
207: if (k == 1) goto L110;
209: if (k == 2) {
211: /* permute the components of Q(:,J) (the information returned by DLAED4 */
212: /* necessary to construct the eigenvectors) according to the permutation */
213: /* stored in INDX, resulting from deflation */
215: for (j = 0; j < k; ++j) {
216: w[0] = q[0+j*ldq];
217: w[1] = q[1+j*ldq];
218: ii = indx[0];
219: q[0+j*ldq] = w[ii-1];
220: ii = indx[1];
221: q[1+j*ldq] = w[ii-1];
222: }
223: goto L110;
224: }
226: /* ....K.GE.3.... */
227: /* Compute updated W (used for computing the eigenvectors corresponding */
228: /* to the previously computed eigenvalues). */
230: PetscCallBLAS("BLAScopy",BLAScopy_(&k, w, &one, s, &one));
232: /* Initialize W(I) = Q(I,I) */
234: i1 = ldq + 1;
235: PetscCallBLAS("BLAScopy",BLAScopy_(&k, q, &i1, w, &one));
236: for (j = 0; j < k; ++j) {
237: for (i = 0; i < j; ++i) {
238: w[i] *= q[i+j*ldq] / (dlamda[i] - dlamda[j]);
239: }
240: for (i = j + 1; i < k; ++i) {
241: w[i] *= q[i+j*ldq] / (dlamda[i] - dlamda[j]);
242: }
243: }
244: for (i = 0; i < k; ++i) {
245: temp = PetscSqrtReal(-w[i]);
246: if (temp<0) temp = -temp;
247: w[i] = (s[i] >= 0) ? temp : -temp;
248: }
250: /* Compute eigenvectors of the modified rank-1 modification (using the */
251: /* vector W). */
253: for (j = 0; j < k; ++j) {
254: for (i = 0; i < k; ++i) {
255: s[i] = w[i] / q[i+j*ldq];
256: }
257: temp = BLASnrm2_(&k, s, &one);
258: for (i = 0; i < k; ++i) {
260: /* apply the permutation resulting from deflation as stored */
261: /* in INDX */
263: ii = indx[i];
264: q[i+j*ldq] = s[ii-1] / temp;
265: }
266: }
268: /* ************************************************************************** */
270: /* ....updating the eigenvectors.... */
272: L110:
274: n2 = n - n1;
275: n12 = ctot[0] + ctot[1];
276: n23 = ctot[1] + ctot[2];
277: if (*(unsigned char *)jobz == 'D') {
279: /* Compute the updated eigenvectors. (NOTE that every call of */
280: /* DGEMM requires three DISTINCT arrays) */
282: /* copy Q(CTOT(1)+1:K,1:K) to S */
284: for (j=0;j<k;j++) for (i=0;i<n23;i++) s[i+j*n23] = q[ctot[0]+i+j*ldq];
285: iq2 = n1 * n12 + 1;
287: if (n23 != 0) {
289: /* multiply the second part of Q2 (the eigenvectors of the */
290: /* lower block) with S and write the result into the lower part of */
291: /* Q, i.e., Q(N1+1:N,1:K) */
293: PetscCallBLAS("BLASgemm",BLASgemm_("N", "N", &n2, &k, &n23, &done,
294: &q2[iq2-1], &n2, s, &n23, &dzero, &q[n1], &ldq));
295: } else {
296: for (j=0;j<k;j++) for (i=0;i<n2;i++) q[n1+i+j*ldq] = 0.0;
297: }
299: /* copy Q(1:CTOT(1)+CTOT(2),1:K) to S */
301: for (j=0;j<k;j++) for (i=0;i<n12;i++) s[i+j*n12] = q[i+j*ldq];
303: if (n12 != 0) {
305: /* multiply the first part of Q2 (the eigenvectors of the */
306: /* upper block) with S and write the result into the upper part of */
307: /* Q, i.e., Q(1:N1,1:K) */
309: PetscCallBLAS("BLASgemm",BLASgemm_("N", "N", &n1, &k, &n12, &done,
310: q2, &n1, s, &n12, &dzero, q, &ldq));
311: } else {
312: for (j=0;j<k;j++) for (i=0;i<n1;i++) q[i+j*ldq] = 0.0;
313: }
314: }
315: PetscFunctionReturn(PETSC_SUCCESS);
316: }