Annotation of rpl/lapack/lapack/dspgvd.f, revision 1.13
1.9 bertrand 1: *> \brief \b DSPGST
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSPGVD + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspgvd.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspgvd.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspgvd.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
22: * LWORK, IWORK, LIWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOBZ, UPLO
26: * INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
27: * ..
28: * .. Array Arguments ..
29: * INTEGER IWORK( * )
30: * DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
31: * $ Z( LDZ, * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
41: *> of a real generalized symmetric-definite eigenproblem, of the form
42: *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
43: *> B are assumed to be symmetric, stored in packed format, and B is also
44: *> positive definite.
45: *> If eigenvectors are desired, it uses a divide and conquer algorithm.
46: *>
47: *> The divide and conquer algorithm makes very mild assumptions about
48: *> floating point arithmetic. It will work on machines with a guard
49: *> digit in add/subtract, or on those binary machines without guard
50: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
51: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
52: *> without guard digits, but we know of none.
53: *> \endverbatim
54: *
55: * Arguments:
56: * ==========
57: *
58: *> \param[in] ITYPE
59: *> \verbatim
60: *> ITYPE is INTEGER
61: *> Specifies the problem type to be solved:
62: *> = 1: A*x = (lambda)*B*x
63: *> = 2: A*B*x = (lambda)*x
64: *> = 3: B*A*x = (lambda)*x
65: *> \endverbatim
66: *>
67: *> \param[in] JOBZ
68: *> \verbatim
69: *> JOBZ is CHARACTER*1
70: *> = 'N': Compute eigenvalues only;
71: *> = 'V': Compute eigenvalues and eigenvectors.
72: *> \endverbatim
73: *>
74: *> \param[in] UPLO
75: *> \verbatim
76: *> UPLO is CHARACTER*1
77: *> = 'U': Upper triangles of A and B are stored;
78: *> = 'L': Lower triangles of A and B are stored.
79: *> \endverbatim
80: *>
81: *> \param[in] N
82: *> \verbatim
83: *> N is INTEGER
84: *> The order of the matrices A and B. N >= 0.
85: *> \endverbatim
86: *>
87: *> \param[in,out] AP
88: *> \verbatim
89: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
90: *> On entry, the upper or lower triangle of the symmetric matrix
91: *> A, packed columnwise in a linear array. The j-th column of A
92: *> is stored in the array AP as follows:
93: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
94: *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
95: *>
96: *> On exit, the contents of AP are destroyed.
97: *> \endverbatim
98: *>
99: *> \param[in,out] BP
100: *> \verbatim
101: *> BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
102: *> On entry, the upper or lower triangle of the symmetric matrix
103: *> B, packed columnwise in a linear array. The j-th column of B
104: *> is stored in the array BP as follows:
105: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
106: *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
107: *>
108: *> On exit, the triangular factor U or L from the Cholesky
109: *> factorization B = U**T*U or B = L*L**T, in the same storage
110: *> format as B.
111: *> \endverbatim
112: *>
113: *> \param[out] W
114: *> \verbatim
115: *> W is DOUBLE PRECISION array, dimension (N)
116: *> If INFO = 0, the eigenvalues in ascending order.
117: *> \endverbatim
118: *>
119: *> \param[out] Z
120: *> \verbatim
121: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
122: *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
123: *> eigenvectors. The eigenvectors are normalized as follows:
124: *> if ITYPE = 1 or 2, Z**T*B*Z = I;
125: *> if ITYPE = 3, Z**T*inv(B)*Z = I.
126: *> If JOBZ = 'N', then Z is not referenced.
127: *> \endverbatim
128: *>
129: *> \param[in] LDZ
130: *> \verbatim
131: *> LDZ is INTEGER
132: *> The leading dimension of the array Z. LDZ >= 1, and if
133: *> JOBZ = 'V', LDZ >= max(1,N).
134: *> \endverbatim
135: *>
136: *> \param[out] WORK
137: *> \verbatim
138: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
139: *> On exit, if INFO = 0, WORK(1) returns the required LWORK.
140: *> \endverbatim
141: *>
142: *> \param[in] LWORK
143: *> \verbatim
144: *> LWORK is INTEGER
145: *> The dimension of the array WORK.
146: *> If N <= 1, LWORK >= 1.
147: *> If JOBZ = 'N' and N > 1, LWORK >= 2*N.
148: *> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
149: *>
150: *> If LWORK = -1, then a workspace query is assumed; the routine
151: *> only calculates the required sizes of the WORK and IWORK
152: *> arrays, returns these values as the first entries of the WORK
153: *> and IWORK arrays, and no error message related to LWORK or
154: *> LIWORK is issued by XERBLA.
155: *> \endverbatim
156: *>
157: *> \param[out] IWORK
158: *> \verbatim
159: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
160: *> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
161: *> \endverbatim
162: *>
163: *> \param[in] LIWORK
164: *> \verbatim
165: *> LIWORK is INTEGER
166: *> The dimension of the array IWORK.
167: *> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
168: *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
169: *>
170: *> If LIWORK = -1, then a workspace query is assumed; the
171: *> routine only calculates the required sizes of the WORK and
172: *> IWORK arrays, returns these values as the first entries of
173: *> the WORK and IWORK arrays, and no error message related to
174: *> LWORK or LIWORK is issued by XERBLA.
175: *> \endverbatim
176: *>
177: *> \param[out] INFO
178: *> \verbatim
179: *> INFO is INTEGER
180: *> = 0: successful exit
181: *> < 0: if INFO = -i, the i-th argument had an illegal value
182: *> > 0: DPPTRF or DSPEVD returned an error code:
183: *> <= N: if INFO = i, DSPEVD failed to converge;
184: *> i off-diagonal elements of an intermediate
185: *> tridiagonal form did not converge to zero;
186: *> > N: if INFO = N + i, for 1 <= i <= N, then the leading
187: *> minor of order i of B is not positive definite.
188: *> The factorization of B could not be completed and
189: *> no eigenvalues or eigenvectors were computed.
190: *> \endverbatim
191: *
192: * Authors:
193: * ========
194: *
195: *> \author Univ. of Tennessee
196: *> \author Univ. of California Berkeley
197: *> \author Univ. of Colorado Denver
198: *> \author NAG Ltd.
199: *
200: *> \date November 2011
201: *
202: *> \ingroup doubleOTHEReigen
203: *
204: *> \par Contributors:
205: * ==================
206: *>
207: *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
208: *
209: * =====================================================================
1.1 bertrand 210: SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
211: $ LWORK, IWORK, LIWORK, INFO )
212: *
1.9 bertrand 213: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 214: * -- LAPACK is a software package provided by Univ. of Tennessee, --
215: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 216: * November 2011
1.1 bertrand 217: *
218: * .. Scalar Arguments ..
219: CHARACTER JOBZ, UPLO
220: INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
221: * ..
222: * .. Array Arguments ..
223: INTEGER IWORK( * )
224: DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
225: $ Z( LDZ, * )
226: * ..
227: *
228: * =====================================================================
229: *
230: * .. Local Scalars ..
231: LOGICAL LQUERY, UPPER, WANTZ
232: CHARACTER TRANS
233: INTEGER J, LIWMIN, LWMIN, NEIG
234: * ..
235: * .. External Functions ..
236: LOGICAL LSAME
237: EXTERNAL LSAME
238: * ..
239: * .. External Subroutines ..
240: EXTERNAL DPPTRF, DSPEVD, DSPGST, DTPMV, DTPSV, XERBLA
241: * ..
242: * .. Intrinsic Functions ..
243: INTRINSIC DBLE, MAX
244: * ..
245: * .. Executable Statements ..
246: *
247: * Test the input parameters.
248: *
249: WANTZ = LSAME( JOBZ, 'V' )
250: UPPER = LSAME( UPLO, 'U' )
251: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
252: *
253: INFO = 0
254: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
255: INFO = -1
256: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
257: INFO = -2
258: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
259: INFO = -3
260: ELSE IF( N.LT.0 ) THEN
261: INFO = -4
262: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
263: INFO = -9
264: END IF
265: *
266: IF( INFO.EQ.0 ) THEN
267: IF( N.LE.1 ) THEN
268: LIWMIN = 1
269: LWMIN = 1
270: ELSE
271: IF( WANTZ ) THEN
272: LIWMIN = 3 + 5*N
273: LWMIN = 1 + 6*N + 2*N**2
274: ELSE
275: LIWMIN = 1
276: LWMIN = 2*N
277: END IF
278: END IF
279: WORK( 1 ) = LWMIN
280: IWORK( 1 ) = LIWMIN
281: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
282: INFO = -11
283: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
284: INFO = -13
285: END IF
286: END IF
287: *
288: IF( INFO.NE.0 ) THEN
289: CALL XERBLA( 'DSPGVD', -INFO )
290: RETURN
291: ELSE IF( LQUERY ) THEN
292: RETURN
293: END IF
294: *
295: * Quick return if possible
296: *
297: IF( N.EQ.0 )
298: $ RETURN
299: *
300: * Form a Cholesky factorization of BP.
301: *
302: CALL DPPTRF( UPLO, N, BP, INFO )
303: IF( INFO.NE.0 ) THEN
304: INFO = N + INFO
305: RETURN
306: END IF
307: *
308: * Transform problem to standard eigenvalue problem and solve.
309: *
310: CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
311: CALL DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
312: $ LIWORK, INFO )
313: LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) )
314: LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) )
315: *
316: IF( WANTZ ) THEN
317: *
318: * Backtransform eigenvectors to the original problem.
319: *
320: NEIG = N
321: IF( INFO.GT.0 )
322: $ NEIG = INFO - 1
323: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
324: *
325: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
1.8 bertrand 326: * backtransform eigenvectors: x = inv(L)**T *y or inv(U)*y
1.1 bertrand 327: *
328: IF( UPPER ) THEN
329: TRANS = 'N'
330: ELSE
331: TRANS = 'T'
332: END IF
333: *
334: DO 10 J = 1, NEIG
335: CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
336: $ 1 )
337: 10 CONTINUE
338: *
339: ELSE IF( ITYPE.EQ.3 ) THEN
340: *
341: * For B*A*x=(lambda)*x;
1.8 bertrand 342: * backtransform eigenvectors: x = L*y or U**T *y
1.1 bertrand 343: *
344: IF( UPPER ) THEN
345: TRANS = 'T'
346: ELSE
347: TRANS = 'N'
348: END IF
349: *
350: DO 20 J = 1, NEIG
351: CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
352: $ 1 )
353: 20 CONTINUE
354: END IF
355: END IF
356: *
357: WORK( 1 ) = LWMIN
358: IWORK( 1 ) = LIWMIN
359: *
360: RETURN
361: *
362: * End of DSPGVD
363: *
364: END
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