1 /* ./src_f77/dspgv.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
dspgv_(integer * itype,char * jobz,char * uplo,integer * n,doublereal * ap,doublereal * bp,doublereal * w,doublereal * z__,integer * ldz,doublereal * work,integer * info,ftnlen jobz_len,ftnlen uplo_len)12 /* Subroutine */ int dspgv_(integer *itype, char *jobz, char *uplo, integer *
13 n, doublereal *ap, doublereal *bp, doublereal *w, doublereal *z__,
14 integer *ldz, doublereal *work, integer *info, ftnlen jobz_len,
15 ftnlen uplo_len)
16 {
17 /* System generated locals */
18 integer z_dim1, z_offset, i__1;
19
20 /* Local variables */
21 static integer j, neig;
22 extern logical lsame_(char *, char *, ftnlen, ftnlen);
23 extern /* Subroutine */ int dspev_(char *, char *, integer *, doublereal *
24 , doublereal *, doublereal *, integer *, doublereal *, integer *,
25 ftnlen, ftnlen);
26 static char trans[1];
27 static logical upper;
28 extern /* Subroutine */ int dtpmv_(char *, char *, char *, integer *,
29 doublereal *, doublereal *, integer *, ftnlen, ftnlen, ftnlen),
30 dtpsv_(char *, char *, char *, integer *, doublereal *,
31 doublereal *, integer *, ftnlen, ftnlen, ftnlen);
32 static logical wantz;
33 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dpptrf_(
34 char *, integer *, doublereal *, integer *, ftnlen), dspgst_(
35 integer *, char *, integer *, doublereal *, doublereal *, integer
36 *, ftnlen);
37
38
39 /* -- LAPACK driver routine (version 3.0) -- */
40 /* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
41 /* Courant Institute, Argonne National Lab, and Rice University */
42 /* September 30, 1994 */
43
44 /* .. Scalar Arguments .. */
45 /* .. */
46 /* .. Array Arguments .. */
47 /* .. */
48
49 /* Purpose */
50 /* ======= */
51
52 /* DSPGV computes all the eigenvalues and, optionally, the eigenvectors */
53 /* of a real generalized symmetric-definite eigenproblem, of the form */
54 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. */
55 /* Here A and B are assumed to be symmetric, stored in packed format, */
56 /* and B is also positive definite. */
57
58 /* Arguments */
59 /* ========= */
60
61 /* ITYPE (input) INTEGER */
62 /* Specifies the problem type to be solved: */
63 /* = 1: A*x = (lambda)*B*x */
64 /* = 2: A*B*x = (lambda)*x */
65 /* = 3: B*A*x = (lambda)*x */
66
67 /* JOBZ (input) CHARACTER*1 */
68 /* = 'N': Compute eigenvalues only; */
69 /* = 'V': Compute eigenvalues and eigenvectors. */
70
71 /* UPLO (input) CHARACTER*1 */
72 /* = 'U': Upper triangles of A and B are stored; */
73 /* = 'L': Lower triangles of A and B are stored. */
74
75 /* N (input) INTEGER */
76 /* The order of the matrices A and B. N >= 0. */
77
78 /* AP (input/output) DOUBLE PRECISION array, dimension */
79 /* (N*(N+1)/2) */
80 /* On entry, the upper or lower triangle of the symmetric matrix */
81 /* A, packed columnwise in a linear array. The j-th column of A */
82 /* is stored in the array AP as follows: */
83 /* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
84 /* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */
85
86 /* On exit, the contents of AP are destroyed. */
87
88 /* BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
89 /* On entry, the upper or lower triangle of the symmetric matrix */
90 /* B, packed columnwise in a linear array. The j-th column of B */
91 /* is stored in the array BP as follows: */
92 /* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; */
93 /* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. */
94
95 /* On exit, the triangular factor U or L from the Cholesky */
96 /* factorization B = U**T*U or B = L*L**T, in the same storage */
97 /* format as B. */
98
99 /* W (output) DOUBLE PRECISION array, dimension (N) */
100 /* If INFO = 0, the eigenvalues in ascending order. */
101
102 /* Z (output) DOUBLE PRECISION array, dimension (LDZ, N) */
103 /* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */
104 /* eigenvectors. The eigenvectors are normalized as follows: */
105 /* if ITYPE = 1 or 2, Z**T*B*Z = I; */
106 /* if ITYPE = 3, Z**T*inv(B)*Z = I. */
107 /* If JOBZ = 'N', then Z is not referenced. */
108
109 /* LDZ (input) INTEGER */
110 /* The leading dimension of the array Z. LDZ >= 1, and if */
111 /* JOBZ = 'V', LDZ >= max(1,N). */
112
113 /* WORK (workspace) DOUBLE PRECISION array, dimension (3*N) */
114
115 /* INFO (output) INTEGER */
116 /* = 0: successful exit */
117 /* < 0: if INFO = -i, the i-th argument had an illegal value */
118 /* > 0: DPPTRF or DSPEV returned an error code: */
119 /* <= N: if INFO = i, DSPEV failed to converge; */
120 /* i off-diagonal elements of an intermediate */
121 /* tridiagonal form did not converge to zero. */
122 /* > N: if INFO = n + i, for 1 <= i <= n, then the leading */
123 /* minor of order i of B is not positive definite. */
124 /* The factorization of B could not be completed and */
125 /* no eigenvalues or eigenvectors were computed. */
126
127 /* ===================================================================== */
128
129 /* .. Local Scalars .. */
130 /* .. */
131 /* .. External Functions .. */
132 /* .. */
133 /* .. External Subroutines .. */
134 /* .. */
135 /* .. Executable Statements .. */
136
137 /* Test the input parameters. */
138
139 /* Parameter adjustments */
140 --ap;
141 --bp;
142 --w;
143 z_dim1 = *ldz;
144 z_offset = 1 + z_dim1;
145 z__ -= z_offset;
146 --work;
147
148 /* Function Body */
149 wantz = lsame_(jobz, "V", (ftnlen)1, (ftnlen)1);
150 upper = lsame_(uplo, "U", (ftnlen)1, (ftnlen)1);
151
152 *info = 0;
153 if (*itype < 0 || *itype > 3) {
154 *info = -1;
155 } else if (! (wantz || lsame_(jobz, "N", (ftnlen)1, (ftnlen)1))) {
156 *info = -2;
157 } else if (! (upper || lsame_(uplo, "L", (ftnlen)1, (ftnlen)1))) {
158 *info = -3;
159 } else if (*n < 0) {
160 *info = -4;
161 } else if (*ldz < 1 || wantz && *ldz < *n) {
162 *info = -9;
163 }
164 if (*info != 0) {
165 i__1 = -(*info);
166 xerbla_("DSPGV ", &i__1, (ftnlen)6);
167 return 0;
168 }
169
170 /* Quick return if possible */
171
172 if (*n == 0) {
173 return 0;
174 }
175
176 /* Form a Cholesky factorization of B. */
177
178 dpptrf_(uplo, n, &bp[1], info, (ftnlen)1);
179 if (*info != 0) {
180 *info = *n + *info;
181 return 0;
182 }
183
184 /* Transform problem to standard eigenvalue problem and solve. */
185
186 dspgst_(itype, uplo, n, &ap[1], &bp[1], info, (ftnlen)1);
187 dspev_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], info,
188 (ftnlen)1, (ftnlen)1);
189
190 if (wantz) {
191
192 /* Backtransform eigenvectors to the original problem. */
193
194 neig = *n;
195 if (*info > 0) {
196 neig = *info - 1;
197 }
198 if (*itype == 1 || *itype == 2) {
199
200 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */
201 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
202
203 if (upper) {
204 *(unsigned char *)trans = 'N';
205 } else {
206 *(unsigned char *)trans = 'T';
207 }
208
209 i__1 = neig;
210 for (j = 1; j <= i__1; ++j) {
211 dtpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 +
212 1], &c__1, (ftnlen)1, (ftnlen)1, (ftnlen)8);
213 /* L10: */
214 }
215
216 } else if (*itype == 3) {
217
218 /* For B*A*x=(lambda)*x; */
219 /* backtransform eigenvectors: x = L*y or U'*y */
220
221 if (upper) {
222 *(unsigned char *)trans = 'T';
223 } else {
224 *(unsigned char *)trans = 'N';
225 }
226
227 i__1 = neig;
228 for (j = 1; j <= i__1; ++j) {
229 dtpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 +
230 1], &c__1, (ftnlen)1, (ftnlen)1, (ftnlen)8);
231 /* L20: */
232 }
233 }
234 }
235 return 0;
236
237 /* End of DSPGV */
238
239 } /* dspgv_ */
240
241