GCC Code Coverage Report

Directory: ./
File: src/sys/classes/ds/impls/hep/bdc/dlaed3m.c
Date: 2025-10-03 04:28:47
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Lines: 63 64 98.4%
Functions: 1 1 100.0%
Branches: 113 210 53.8%
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1 /*
2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 SLEPc - Scalable Library for Eigenvalue Problem Computations
4 Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5
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 */
13
14 #include <slepc/private/dsimpl.h>
15 #include <slepcblaslapack.h>
16
17 105 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 */
29
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 /* *************************************************** */
35
36 /* Purpose */
37 /* ======= */
38
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. */
45
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. */
52
53 /* Arguments */
54 /* ========= */
55
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. */
60
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) */
66
67 /* K (input) INTEGER */
68 /* The number of terms in the rational function to be solved by */
69 /* DLAED4. 0 <= K <= N. */
70
71 /* N (input) INTEGER */
72 /* The number of rows and columns in the Q matrix. */
73 /* N >= K (deflation may result in N>K). */
74
75 /* N1 (input) INTEGER */
76 /* The location of the last eigenvalue in the leading submatrix. */
77 /* min(1,N) <= N1 <= max(1,N-1). */
78
79 /* D (output) DOUBLE PRECISION array, dimension (N) */
80 /* D(I) contains the updated eigenvalues for */
81 /* 1 <= I <= K. */
82
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. */
87
88 /* LDQ (input) INTEGER */
89 /* The leading dimension of the array Q. LDQ >= max(1,N). */
90
91 /* RHO (input) DOUBLE PRECISION */
92 /* The value of the parameter in the rank one update equation. */
93 /* RHO >= 0 required. */
94
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. */
101
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. */
105
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. */
111
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. */
116
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. */
121
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 ! */
128
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 */
133
134 /* Further Details */
135 /* =============== */
136
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) */
143
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. */
148
149 /* ===================================================================== */
150
151 105 PetscReal temp, done = 1.0, dzero = 0.0;
152 105 PetscBLASInt i, j, n2, n12, ii, n23, iq2, i1, one=1;
153
154
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 105 PetscFunctionBegin;
155 105 *info = 0;
156
157
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 105 if (k < 0) *info = -3;
158
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 105 else if (n < k) *info = -4;
159
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 105 else if (n1 < PetscMin(1,n) || n1 > PetscMax(1,n)) *info = -5;
160
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 105 else if (ldq < PetscMax(1,n)) *info = -8;
161
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 105 else if (rho < 0.) *info = -9;
162
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 105 PetscCheck(!*info,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong argument %" PetscBLASInt_FMT " in DLAED3M",-(*info));
163
164 /* Quick return if possible */
165
166
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 105 if (k == 0) PetscFunctionReturn(PETSC_SUCCESS);
167
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. */
184
185
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 905 for (i = 0; i < k; ++i) {
186 800 dlamda[i] = LAPACKlamc3_(&dlamda[i], &dlamda[i]) - dlamda[i];
187 }
188
189
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 905 for (j = 1; j <= k; ++j) {
190
191 /* ....calling DLAED4 for eigenpair J.... */
192
193
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 800 PetscCallBLAS("LAPACKlaed4",LAPACKlaed4_(&k, &j, dlamda, w, &q[(j-1)*ldq], &rho, &d[j-1], info));
194
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 800 SlepcCheckLapackInfo("laed4",*info);
195
196
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 800 if (j < k) {
197
198 /* If the zero finder terminated properly, but the computed */
199 /* eigenvalues are not ordered, issue an error statement */
200 /* but continue computation. */
201
202
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 695 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
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 800 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 }
206
207
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 105 if (k == 1) goto L110;
208
209
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 105 if (k == 2) {
210
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 */
214
215
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 30 for (j = 0; j < k; ++j) {
216 20 w[0] = q[0+j*ldq];
217 20 w[1] = q[1+j*ldq];
218 20 ii = indx[0];
219 20 q[0+j*ldq] = w[ii-1];
220 20 ii = indx[1];
221 20 q[1+j*ldq] = w[ii-1];
222 }
223 10 goto L110;
224 }
225
226 /* ....K.GE.3.... */
227 /* Compute updated W (used for computing the eigenvectors corresponding */
228 /* to the previously computed eigenvalues). */
229
230
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 95 PetscCallBLAS("BLAScopy",BLAScopy_(&k, w, &one, s, &one));
231
232 /* Initialize W(I) = Q(I,I) */
233
234 95 i1 = ldq + 1;
235
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 95 PetscCallBLAS("BLAScopy",BLAScopy_(&k, q, &i1, w, &one));
236
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 875 for (j = 0; j < k; ++j) {
237
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 4260 for (i = 0; i < j; ++i) {
238 3480 w[i] *= q[i+j*ldq] / (dlamda[i] - dlamda[j]);
239 }
240
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 4260 for (i = j + 1; i < k; ++i) {
241 3480 w[i] *= q[i+j*ldq] / (dlamda[i] - dlamda[j]);
242 }
243 }
244
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 875 for (i = 0; i < k; ++i) {
245 780 temp = PetscSqrtReal(-w[i]);
246
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 780 if (temp<0) temp = -temp;
247
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 780 w[i] = (s[i] >= 0) ? temp : -temp;
248 }
249
250 /* Compute eigenvectors of the modified rank-1 modification (using the */
251 /* vector W). */
252
253
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254
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 8520 for (i = 0; i < k; ++i) {
255 7740 s[i] = w[i] / q[i+j*ldq];
256 }
257 780 temp = BLASnrm2_(&k, s, &one);
258
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 9300 for (i = 0; i < k; ++i) {
259
260 /* apply the permutation resulting from deflation as stored */
261 /* in INDX */
262
263 7740 ii = indx[i];
264 7740 q[i+j*ldq] = s[ii-1] / temp;
265 }
266 }
267
268 /* ************************************************************************** */
269
270 /* ....updating the eigenvectors.... */
271
272 95 L110:
273
274 105 n2 = n - n1;
275 105 n12 = ctot[0] + ctot[1];
276 105 n23 = ctot[1] + ctot[2];
277
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 105 if (*(unsigned char *)jobz == 'D') {
278
279 /* Compute the updated eigenvectors. (NOTE that every call of */
280 /* DGEMM requires three DISTINCT arrays) */
281
282 /* copy Q(CTOT(1)+1:K,1:K) to S */
283
284
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 2615 for (j=0;j<k;j++) for (i=0;i<n23;i++) s[i+j*n23] = q[ctot[0]+i+j*ldq];
285 105 iq2 = n1 * n12 + 1;
286
287
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 105 if (n23 != 0) {
288
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) */
292
293
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 35 PetscCallBLAS("BLASgemm",BLASgemm_("N", "N", &n2, &k, &n23, &done,
294 &q2[iq2-1], &n2, s, &n23, &dzero, &q[n1], &ldq));
295 } else {
296
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 600 for (j=0;j<k;j++) for (i=0;i<n2;i++) q[n1+i+j*ldq] = 0.0;
297 }
298
299 /* copy Q(1:CTOT(1)+CTOT(2),1:K) to S */
300
301
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 7785 for (j=0;j<k;j++) for (i=0;i<n12;i++) s[i+j*n12] = q[i+j*ldq];
302
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 105 if (n12 != 0) {
304
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) */
308
309
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 105 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
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 21 PetscFunctionReturn(PETSC_SUCCESS);
316 }
317