1 /* ./src_f77/slatdf.f -- translated by f2c (version 20030320).
2 You must link the resulting object file with the libraries:
3 -lf2c -lm (in that order)
4 */
5
6 #include <punc/vf2c.h>
7
8 /* Table of constant values */
9
10 static integer c__1 = 1;
11 static integer c_n1 = -1;
12 static real c_b23 = 1.f;
13 static real c_b37 = -1.f;
14
slatdf_(integer * ijob,integer * n,real * z__,integer * ldz,real * rhs,real * rdsum,real * rdscal,integer * ipiv,integer * jpiv)15 /* Subroutine */ int slatdf_(integer *ijob, integer *n, real *z__, integer *
16 ldz, real *rhs, real *rdsum, real *rdscal, integer *ipiv, integer *
17 jpiv)
18 {
19 /* System generated locals */
20 integer z_dim1, z_offset, i__1, i__2;
21 real r__1;
22
23 /* Builtin functions */
24 double sqrt(doublereal);
25
26 /* Local variables */
27 static integer i__, j, k;
28 static real bm, bp, xm[8], xp[8];
29 static integer info;
30 static real temp;
31 extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
32 static real work[32];
33 extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
34 static real pmone;
35 extern doublereal sasum_(integer *, real *, integer *);
36 static real sminu;
37 static integer iwork[8];
38 extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
39 integer *), saxpy_(integer *, real *, real *, integer *, real *,
40 integer *);
41 static real splus;
42 extern /* Subroutine */ int sgesc2_(integer *, real *, integer *, real *,
43 integer *, integer *, real *), sgecon_(char *, integer *, real *,
44 integer *, real *, real *, real *, integer *, integer *, ftnlen),
45 slassq_(integer *, real *, integer *, real *, real *), slaswp_(
46 integer *, real *, integer *, integer *, integer *, integer *,
47 integer *);
48
49
50 /* -- LAPACK auxiliary routine (version 3.0) -- */
51 /* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
52 /* Courant Institute, Argonne National Lab, and Rice University */
53 /* June 30, 1999 */
54
55 /* .. Scalar Arguments .. */
56 /* .. */
57 /* .. Array Arguments .. */
58 /* .. */
59
60 /* Purpose */
61 /* ======= */
62
63 /* SLATDF uses the LU factorization of the n-by-n matrix Z computed by */
64 /* SGETC2 and computes a contribution to the reciprocal Dif-estimate */
65 /* by solving Z * x = b for x, and choosing the r.h.s. b such that */
66 /* the norm of x is as large as possible. On entry RHS = b holds the */
67 /* contribution from earlier solved sub-systems, and on return RHS = x. */
68
69 /* The factorization of Z returned by SGETC2 has the form Z = P*L*U*Q, */
70 /* where P and Q are permutation matrices. L is lower triangular with */
71 /* unit diagonal elements and U is upper triangular. */
72
73 /* Arguments */
74 /* ========= */
75
76 /* IJOB (input) INTEGER */
77 /* IJOB = 2: First compute an approximative null-vector e */
78 /* of Z using SGECON, e is normalized and solve for */
79 /* Zx = +-e - f with the sign giving the greater value */
80 /* of 2-norm(x). About 5 times as expensive as Default. */
81 /* IJOB .ne. 2: Local look ahead strategy where all entries of */
82 /* the r.h.s. b is choosen as either +1 or -1 (Default). */
83
84 /* N (input) INTEGER */
85 /* The number of columns of the matrix Z. */
86
87 /* Z (input) REAL array, dimension (LDZ, N) */
88 /* On entry, the LU part of the factorization of the n-by-n */
89 /* matrix Z computed by SGETC2: Z = P * L * U * Q */
90
91 /* LDZ (input) INTEGER */
92 /* The leading dimension of the array Z. LDA >= max(1, N). */
93
94 /* RHS (input/output) REAL array, dimension N. */
95 /* On entry, RHS contains contributions from other subsystems. */
96 /* On exit, RHS contains the solution of the subsystem with */
97 /* entries acoording to the value of IJOB (see above). */
98
99 /* RDSUM (input/output) REAL */
100 /* On entry, the sum of squares of computed contributions to */
101 /* the Dif-estimate under computation by STGSYL, where the */
102 /* scaling factor RDSCAL (see below) has been factored out. */
103 /* On exit, the corresponding sum of squares updated with the */
104 /* contributions from the current sub-system. */
105 /* If TRANS = 'T' RDSUM is not touched. */
106 /* NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL. */
107
108 /* RDSCAL (input/output) REAL */
109 /* On entry, scaling factor used to prevent overflow in RDSUM. */
110 /* On exit, RDSCAL is updated w.r.t. the current contributions */
111 /* in RDSUM. */
112 /* If TRANS = 'T', RDSCAL is not touched. */
113 /* NOTE: RDSCAL only makes sense when STGSY2 is called by */
114 /* STGSYL. */
115
116 /* IPIV (input) INTEGER array, dimension (N). */
117 /* The pivot indices; for 1 <= i <= N, row i of the */
118 /* matrix has been interchanged with row IPIV(i). */
119
120 /* JPIV (input) INTEGER array, dimension (N). */
121 /* The pivot indices; for 1 <= j <= N, column j of the */
122 /* matrix has been interchanged with column JPIV(j). */
123
124 /* Further Details */
125 /* =============== */
126
127 /* Based on contributions by */
128 /* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
129 /* Umea University, S-901 87 Umea, Sweden. */
130
131 /* This routine is a further developed implementation of algorithm */
132 /* BSOLVE in [1] using complete pivoting in the LU factorization. */
133
134 /* [1] Bo Kagstrom and Lars Westin, */
135 /* Generalized Schur Methods with Condition Estimators for */
136 /* Solving the Generalized Sylvester Equation, IEEE Transactions */
137 /* on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751. */
138
139 /* [2] Peter Poromaa, */
140 /* On Efficient and Robust Estimators for the Separation */
141 /* between two Regular Matrix Pairs with Applications in */
142 /* Condition Estimation. Report IMINF-95.05, Departement of */
143 /* Computing Science, Umea University, S-901 87 Umea, Sweden, 1995. */
144
145 /* ===================================================================== */
146
147 /* .. Parameters .. */
148 /* .. */
149 /* .. Local Scalars .. */
150 /* .. */
151 /* .. Local Arrays .. */
152 /* .. */
153 /* .. External Subroutines .. */
154 /* .. */
155 /* .. External Functions .. */
156 /* .. */
157 /* .. Intrinsic Functions .. */
158 /* .. */
159 /* .. Executable Statements .. */
160
161 /* Parameter adjustments */
162 z_dim1 = *ldz;
163 z_offset = 1 + z_dim1;
164 z__ -= z_offset;
165 --rhs;
166 --ipiv;
167 --jpiv;
168
169 /* Function Body */
170 if (*ijob != 2) {
171
172 /* Apply permutations IPIV to RHS */
173
174 i__1 = *n - 1;
175 slaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &ipiv[1], &c__1);
176
177 /* Solve for L-part choosing RHS either to +1 or -1. */
178
179 pmone = -1.f;
180
181 i__1 = *n - 1;
182 for (j = 1; j <= i__1; ++j) {
183 bp = rhs[j] + 1.f;
184 bm = rhs[j] - 1.f;
185 splus = 1.f;
186
187 /* Look-ahead for L-part RHS(1:N-1) = + or -1, SPLUS and */
188 /* SMIN computed more efficiently than in BSOLVE [1]. */
189
190 i__2 = *n - j;
191 splus += sdot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &z__[j + 1
192 + j * z_dim1], &c__1);
193 i__2 = *n - j;
194 sminu = sdot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
195 &c__1);
196 splus *= rhs[j];
197 if (splus > sminu) {
198 rhs[j] = bp;
199 } else if (sminu > splus) {
200 rhs[j] = bm;
201 } else {
202
203 /* In this case the updating sums are equal and we can */
204 /* choose RHS(J) +1 or -1. The first time this happens */
205 /* we choose -1, thereafter +1. This is a simple way to */
206 /* get good estimates of matrices like Byers well-known */
207 /* example (see [1]). (Not done in BSOLVE.) */
208
209 rhs[j] += pmone;
210 pmone = 1.f;
211 }
212
213 /* Compute the remaining r.h.s. */
214
215 temp = -rhs[j];
216 i__2 = *n - j;
217 saxpy_(&i__2, &temp, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
218 &c__1);
219
220 /* L10: */
221 }
222
223 /* Solve for U-part, look-ahead for RHS(N) = +-1. This is not done */
224 /* in BSOLVE and will hopefully give us a better estimate because */
225 /* any ill-conditioning of the original matrix is transfered to U */
226 /* and not to L. U(N, N) is an approximation to sigma_min(LU). */
227
228 i__1 = *n - 1;
229 scopy_(&i__1, &rhs[1], &c__1, xp, &c__1);
230 xp[*n - 1] = rhs[*n] + 1.f;
231 rhs[*n] += -1.f;
232 splus = 0.f;
233 sminu = 0.f;
234 for (i__ = *n; i__ >= 1; --i__) {
235 temp = 1.f / z__[i__ + i__ * z_dim1];
236 xp[i__ - 1] *= temp;
237 rhs[i__] *= temp;
238 i__1 = *n;
239 for (k = i__ + 1; k <= i__1; ++k) {
240 xp[i__ - 1] -= xp[k - 1] * (z__[i__ + k * z_dim1] * temp);
241 rhs[i__] -= rhs[k] * (z__[i__ + k * z_dim1] * temp);
242 /* L20: */
243 }
244 splus += (r__1 = xp[i__ - 1], dabs(r__1));
245 sminu += (r__1 = rhs[i__], dabs(r__1));
246 /* L30: */
247 }
248 if (splus > sminu) {
249 scopy_(n, xp, &c__1, &rhs[1], &c__1);
250 }
251
252 /* Apply the permutations JPIV to the computed solution (RHS) */
253
254 i__1 = *n - 1;
255 slaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);
256
257 /* Compute the sum of squares */
258
259 slassq_(n, &rhs[1], &c__1, rdscal, rdsum);
260
261 } else {
262
263 /* IJOB = 2, Compute approximate nullvector XM of Z */
264
265 sgecon_("I", n, &z__[z_offset], ldz, &c_b23, &temp, work, iwork, &
266 info, (ftnlen)1);
267 scopy_(n, &work[*n], &c__1, xm, &c__1);
268
269 /* Compute RHS */
270
271 i__1 = *n - 1;
272 slaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
273 temp = 1.f / sqrt(sdot_(n, xm, &c__1, xm, &c__1));
274 sscal_(n, &temp, xm, &c__1);
275 scopy_(n, xm, &c__1, xp, &c__1);
276 saxpy_(n, &c_b23, &rhs[1], &c__1, xp, &c__1);
277 saxpy_(n, &c_b37, xm, &c__1, &rhs[1], &c__1);
278 sgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &temp);
279 sgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &temp);
280 if (sasum_(n, xp, &c__1) > sasum_(n, &rhs[1], &c__1)) {
281 scopy_(n, xp, &c__1, &rhs[1], &c__1);
282 }
283
284 /* Compute the sum of squares */
285
286 slassq_(n, &rhs[1], &c__1, rdscal, rdsum);
287
288 }
289
290 return 0;
291
292 /* End of SLATDF */
293
294 } /* slatdf_ */
295
296