1 /* ./src_f77/zhpgvx.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
zhpgvx_(integer * itype,char * jobz,char * range,char * uplo,integer * n,doublecomplex * ap,doublecomplex * bp,doublereal * vl,doublereal * vu,integer * il,integer * iu,doublereal * abstol,integer * m,doublereal * w,doublecomplex * z__,integer * ldz,doublecomplex * work,doublereal * rwork,integer * iwork,integer * ifail,integer * info,ftnlen jobz_len,ftnlen range_len,ftnlen uplo_len)12 /* Subroutine */ int zhpgvx_(integer *itype, char *jobz, char *range, char *
13 uplo, integer *n, doublecomplex *ap, doublecomplex *bp, doublereal *
14 vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol,
15 integer *m, doublereal *w, doublecomplex *z__, integer *ldz,
16 doublecomplex *work, doublereal *rwork, integer *iwork, integer *
17 ifail, integer *info, ftnlen jobz_len, ftnlen range_len, ftnlen
18 uplo_len)
19 {
20 /* System generated locals */
21 integer z_dim1, z_offset, i__1;
22
23 /* Local variables */
24 static integer j;
25 extern logical lsame_(char *, char *, ftnlen, ftnlen);
26 static char trans[1];
27 static logical upper, wantz;
28 extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *,
29 doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen,
30 ftnlen), ztpsv_(char *, char *, char *, integer *, doublecomplex *
31 , doublecomplex *, integer *, ftnlen, ftnlen, ftnlen);
32 static logical alleig, indeig, valeig;
33 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), zhpgst_(
34 integer *, char *, integer *, doublecomplex *, doublecomplex *,
35 integer *, ftnlen), zhpevx_(char *, char *, char *, integer *,
36 doublecomplex *, doublereal *, doublereal *, integer *, integer *,
37 doublereal *, integer *, doublereal *, doublecomplex *, integer *
38 , doublecomplex *, doublereal *, integer *, integer *, integer *,
39 ftnlen, ftnlen, ftnlen), zpptrf_(char *, integer *, doublecomplex
40 *, integer *, ftnlen);
41
42
43 /* -- LAPACK driver routine (version 3.0) -- */
44 /* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
45 /* Courant Institute, Argonne National Lab, and Rice University */
46 /* June 30, 1999 */
47
48 /* .. Scalar Arguments .. */
49 /* .. */
50 /* .. Array Arguments .. */
51 /* .. */
52
53 /* Purpose */
54 /* ======= */
55
56 /* ZHPGVX computes selected eigenvalues and, optionally, eigenvectors */
57 /* of a complex generalized Hermitian-definite eigenproblem, of the form */
58 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and */
59 /* B are assumed to be Hermitian, stored in packed format, and B is also */
60 /* positive definite. Eigenvalues and eigenvectors can be selected by */
61 /* specifying either a range of values or a range of indices for the */
62 /* desired eigenvalues. */
63
64 /* Arguments */
65 /* ========= */
66
67 /* ITYPE (input) INTEGER */
68 /* Specifies the problem type to be solved: */
69 /* = 1: A*x = (lambda)*B*x */
70 /* = 2: A*B*x = (lambda)*x */
71 /* = 3: B*A*x = (lambda)*x */
72
73 /* JOBZ (input) CHARACTER*1 */
74 /* = 'N': Compute eigenvalues only; */
75 /* = 'V': Compute eigenvalues and eigenvectors. */
76
77 /* RANGE (input) CHARACTER*1 */
78 /* = 'A': all eigenvalues will be found; */
79 /* = 'V': all eigenvalues in the half-open interval (VL,VU] */
80 /* will be found; */
81 /* = 'I': the IL-th through IU-th eigenvalues will be found. */
82
83 /* UPLO (input) CHARACTER*1 */
84 /* = 'U': Upper triangles of A and B are stored; */
85 /* = 'L': Lower triangles of A and B are stored. */
86
87 /* N (input) INTEGER */
88 /* The order of the matrices A and B. N >= 0. */
89
90 /* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) */
91 /* On entry, the upper or lower triangle of the Hermitian matrix */
92 /* A, packed columnwise in a linear array. The j-th column of A */
93 /* is stored in the array AP as follows: */
94 /* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
95 /* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */
96
97 /* On exit, the contents of AP are destroyed. */
98
99 /* BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) */
100 /* On entry, the upper or lower triangle of the Hermitian matrix */
101 /* B, packed columnwise in a linear array. The j-th column of B */
102 /* is stored in the array BP as follows: */
103 /* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; */
104 /* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. */
105
106 /* On exit, the triangular factor U or L from the Cholesky */
107 /* factorization B = U**H*U or B = L*L**H, in the same storage */
108 /* format as B. */
109
110 /* VL (input) DOUBLE PRECISION */
111 /* VU (input) DOUBLE PRECISION */
112 /* If RANGE='V', the lower and upper bounds of the interval to */
113 /* be searched for eigenvalues. VL < VU. */
114 /* Not referenced if RANGE = 'A' or 'I'. */
115
116 /* IL (input) INTEGER */
117 /* IU (input) INTEGER */
118 /* If RANGE='I', the indices (in ascending order) of the */
119 /* smallest and largest eigenvalues to be returned. */
120 /* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
121 /* Not referenced if RANGE = 'A' or 'V'. */
122
123 /* ABSTOL (input) DOUBLE PRECISION */
124 /* The absolute error tolerance for the eigenvalues. */
125 /* An approximate eigenvalue is accepted as converged */
126 /* when it is determined to lie in an interval [a,b] */
127 /* of width less than or equal to */
128
129 /* ABSTOL + EPS * max( |a|,|b| ) , */
130
131 /* where EPS is the machine precision. If ABSTOL is less than */
132 /* or equal to zero, then EPS*|T| will be used in its place, */
133 /* where |T| is the 1-norm of the tridiagonal matrix obtained */
134 /* by reducing AP to tridiagonal form. */
135
136 /* Eigenvalues will be computed most accurately when ABSTOL is */
137 /* set to twice the underflow threshold 2*DLAMCH('S'), not zero. */
138 /* If this routine returns with INFO>0, indicating that some */
139 /* eigenvectors did not converge, try setting ABSTOL to */
140 /* 2*DLAMCH('S'). */
141
142 /* M (output) INTEGER */
143 /* The total number of eigenvalues found. 0 <= M <= N. */
144 /* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */
145
146 /* W (output) DOUBLE PRECISION array, dimension (N) */
147 /* On normal exit, the first M elements contain the selected */
148 /* eigenvalues in ascending order. */
149
150 /* Z (output) COMPLEX*16 array, dimension (LDZ, N) */
151 /* If JOBZ = 'N', then Z is not referenced. */
152 /* If JOBZ = 'V', then if INFO = 0, the first M columns of Z */
153 /* contain the orthonormal eigenvectors of the matrix A */
154 /* corresponding to the selected eigenvalues, with the i-th */
155 /* column of Z holding the eigenvector associated with W(i). */
156 /* The eigenvectors are normalized as follows: */
157 /* if ITYPE = 1 or 2, Z**H*B*Z = I; */
158 /* if ITYPE = 3, Z**H*inv(B)*Z = I. */
159
160 /* If an eigenvector fails to converge, then that column of Z */
161 /* contains the latest approximation to the eigenvector, and the */
162 /* index of the eigenvector is returned in IFAIL. */
163 /* Note: the user must ensure that at least max(1,M) columns are */
164 /* supplied in the array Z; if RANGE = 'V', the exact value of M */
165 /* is not known in advance and an upper bound must be used. */
166
167 /* LDZ (input) INTEGER */
168 /* The leading dimension of the array Z. LDZ >= 1, and if */
169 /* JOBZ = 'V', LDZ >= max(1,N). */
170
171 /* WORK (workspace) COMPLEX*16 array, dimension (2*N) */
172
173 /* RWORK (workspace) DOUBLE PRECISION array, dimension (7*N) */
174
175 /* IWORK (workspace) INTEGER array, dimension (5*N) */
176
177 /* IFAIL (output) INTEGER array, dimension (N) */
178 /* If JOBZ = 'V', then if INFO = 0, the first M elements of */
179 /* IFAIL are zero. If INFO > 0, then IFAIL contains the */
180 /* indices of the eigenvectors that failed to converge. */
181 /* If JOBZ = 'N', then IFAIL is not referenced. */
182
183 /* INFO (output) INTEGER */
184 /* = 0: successful exit */
185 /* < 0: if INFO = -i, the i-th argument had an illegal value */
186 /* > 0: ZPPTRF or ZHPEVX returned an error code: */
187 /* <= N: if INFO = i, ZHPEVX failed to converge; */
188 /* i eigenvectors failed to converge. Their indices */
189 /* are stored in array IFAIL. */
190 /* > N: if INFO = N + i, for 1 <= i <= n, then the leading */
191 /* minor of order i of B is not positive definite. */
192 /* The factorization of B could not be completed and */
193 /* no eigenvalues or eigenvectors were computed. */
194
195 /* Further Details */
196 /* =============== */
197
198 /* Based on contributions by */
199 /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
200
201 /* ===================================================================== */
202
203 /* .. Local Scalars .. */
204 /* .. */
205 /* .. External Functions .. */
206 /* .. */
207 /* .. External Subroutines .. */
208 /* .. */
209 /* .. Intrinsic Functions .. */
210 /* .. */
211 /* .. Executable Statements .. */
212
213 /* Test the input parameters. */
214
215 /* Parameter adjustments */
216 --ap;
217 --bp;
218 --w;
219 z_dim1 = *ldz;
220 z_offset = 1 + z_dim1;
221 z__ -= z_offset;
222 --work;
223 --rwork;
224 --iwork;
225 --ifail;
226
227 /* Function Body */
228 wantz = lsame_(jobz, "V", (ftnlen)1, (ftnlen)1);
229 upper = lsame_(uplo, "U", (ftnlen)1, (ftnlen)1);
230 alleig = lsame_(range, "A", (ftnlen)1, (ftnlen)1);
231 valeig = lsame_(range, "V", (ftnlen)1, (ftnlen)1);
232 indeig = lsame_(range, "I", (ftnlen)1, (ftnlen)1);
233
234 *info = 0;
235 if (*itype < 0 || *itype > 3) {
236 *info = -1;
237 } else if (! (wantz || lsame_(jobz, "N", (ftnlen)1, (ftnlen)1))) {
238 *info = -2;
239 } else if (! (alleig || valeig || indeig)) {
240 *info = -3;
241 } else if (! (upper || lsame_(uplo, "L", (ftnlen)1, (ftnlen)1))) {
242 *info = -4;
243 } else if (*n < 0) {
244 *info = -5;
245 } else if (valeig && *n > 0 && *vu <= *vl) {
246 *info = -9;
247 } else if (indeig && *il < 1) {
248 *info = -10;
249 } else if (indeig && (*iu < min(*n,*il) || *iu > *n)) {
250 *info = -11;
251 } else if (*ldz < 1 || wantz && *ldz < *n) {
252 *info = -16;
253 }
254 if (*info != 0) {
255 i__1 = -(*info);
256 xerbla_("ZHPGVX", &i__1, (ftnlen)6);
257 return 0;
258 }
259
260 /* Quick return if possible */
261
262 if (*n == 0) {
263 return 0;
264 }
265
266 /* Form a Cholesky factorization of B. */
267
268 zpptrf_(uplo, n, &bp[1], info, (ftnlen)1);
269 if (*info != 0) {
270 *info = *n + *info;
271 return 0;
272 }
273
274 /* Transform problem to standard eigenvalue problem and solve. */
275
276 zhpgst_(itype, uplo, n, &ap[1], &bp[1], info, (ftnlen)1);
277 zhpevx_(jobz, range, uplo, n, &ap[1], vl, vu, il, iu, abstol, m, &w[1], &
278 z__[z_offset], ldz, &work[1], &rwork[1], &iwork[1], &ifail[1],
279 info, (ftnlen)1, (ftnlen)1, (ftnlen)1);
280
281 if (wantz) {
282
283 /* Backtransform eigenvectors to the original problem. */
284
285 if (*info > 0) {
286 *m = *info - 1;
287 }
288 if (*itype == 1 || *itype == 2) {
289
290 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */
291 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
292
293 if (upper) {
294 *(unsigned char *)trans = 'N';
295 } else {
296 *(unsigned char *)trans = 'C';
297 }
298
299 i__1 = *m;
300 for (j = 1; j <= i__1; ++j) {
301 ztpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 +
302 1], &c__1, (ftnlen)1, (ftnlen)1, (ftnlen)8);
303 /* L10: */
304 }
305
306 } else if (*itype == 3) {
307
308 /* For B*A*x=(lambda)*x; */
309 /* backtransform eigenvectors: x = L*y or U'*y */
310
311 if (upper) {
312 *(unsigned char *)trans = 'C';
313 } else {
314 *(unsigned char *)trans = 'N';
315 }
316
317 i__1 = *m;
318 for (j = 1; j <= i__1; ++j) {
319 ztpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 +
320 1], &c__1, (ftnlen)1, (ftnlen)1, (ftnlen)8);
321 /* L20: */
322 }
323 }
324 }
325
326 return 0;
327
328 /* End of ZHPGVX */
329
330 } /* zhpgvx_ */
331
332