Annotation of rpl/lapack/lapack/dspgvd.f, revision 1.2
1.1 bertrand 1: SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
2: $ LWORK, IWORK, LIWORK, INFO )
3: *
4: * -- LAPACK driver routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
8: *
9: * .. Scalar Arguments ..
10: CHARACTER JOBZ, UPLO
11: INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
12: * ..
13: * .. Array Arguments ..
14: INTEGER IWORK( * )
15: DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
16: $ Z( LDZ, * )
17: * ..
18: *
19: * Purpose
20: * =======
21: *
22: * DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
23: * of a real generalized symmetric-definite eigenproblem, of the form
24: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
25: * B are assumed to be symmetric, stored in packed format, and B is also
26: * positive definite.
27: * If eigenvectors are desired, it uses a divide and conquer algorithm.
28: *
29: * The divide and conquer algorithm makes very mild assumptions about
30: * floating point arithmetic. It will work on machines with a guard
31: * digit in add/subtract, or on those binary machines without guard
32: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
33: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
34: * without guard digits, but we know of none.
35: *
36: * Arguments
37: * =========
38: *
39: * ITYPE (input) INTEGER
40: * Specifies the problem type to be solved:
41: * = 1: A*x = (lambda)*B*x
42: * = 2: A*B*x = (lambda)*x
43: * = 3: B*A*x = (lambda)*x
44: *
45: * JOBZ (input) CHARACTER*1
46: * = 'N': Compute eigenvalues only;
47: * = 'V': Compute eigenvalues and eigenvectors.
48: *
49: * UPLO (input) CHARACTER*1
50: * = 'U': Upper triangles of A and B are stored;
51: * = 'L': Lower triangles of A and B are stored.
52: *
53: * N (input) INTEGER
54: * The order of the matrices A and B. N >= 0.
55: *
56: * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
57: * On entry, the upper or lower triangle of the symmetric matrix
58: * A, packed columnwise in a linear array. The j-th column of A
59: * is stored in the array AP as follows:
60: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
61: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
62: *
63: * On exit, the contents of AP are destroyed.
64: *
65: * BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
66: * On entry, the upper or lower triangle of the symmetric matrix
67: * B, packed columnwise in a linear array. The j-th column of B
68: * is stored in the array BP as follows:
69: * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
70: * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
71: *
72: * On exit, the triangular factor U or L from the Cholesky
73: * factorization B = U**T*U or B = L*L**T, in the same storage
74: * format as B.
75: *
76: * W (output) DOUBLE PRECISION array, dimension (N)
77: * If INFO = 0, the eigenvalues in ascending order.
78: *
79: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
80: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
81: * eigenvectors. The eigenvectors are normalized as follows:
82: * if ITYPE = 1 or 2, Z**T*B*Z = I;
83: * if ITYPE = 3, Z**T*inv(B)*Z = I.
84: * If JOBZ = 'N', then Z is not referenced.
85: *
86: * LDZ (input) INTEGER
87: * The leading dimension of the array Z. LDZ >= 1, and if
88: * JOBZ = 'V', LDZ >= max(1,N).
89: *
90: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
91: * On exit, if INFO = 0, WORK(1) returns the required LWORK.
92: *
93: * LWORK (input) INTEGER
94: * The dimension of the array WORK.
95: * If N <= 1, LWORK >= 1.
96: * If JOBZ = 'N' and N > 1, LWORK >= 2*N.
97: * If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
98: *
99: * If LWORK = -1, then a workspace query is assumed; the routine
100: * only calculates the required sizes of the WORK and IWORK
101: * arrays, returns these values as the first entries of the WORK
102: * and IWORK arrays, and no error message related to LWORK or
103: * LIWORK is issued by XERBLA.
104: *
105: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
106: * On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
107: *
108: * LIWORK (input) INTEGER
109: * The dimension of the array IWORK.
110: * If JOBZ = 'N' or N <= 1, LIWORK >= 1.
111: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
112: *
113: * If LIWORK = -1, then a workspace query is assumed; the
114: * routine only calculates the required sizes of the WORK and
115: * IWORK arrays, returns these values as the first entries of
116: * the WORK and IWORK arrays, and no error message related to
117: * LWORK or LIWORK is issued by XERBLA.
118: *
119: * INFO (output) INTEGER
120: * = 0: successful exit
121: * < 0: if INFO = -i, the i-th argument had an illegal value
122: * > 0: DPPTRF or DSPEVD returned an error code:
123: * <= N: if INFO = i, DSPEVD failed to converge;
124: * i off-diagonal elements of an intermediate
125: * tridiagonal form did not converge to zero;
126: * > N: if INFO = N + i, for 1 <= i <= N, then the leading
127: * minor of order i of B is not positive definite.
128: * The factorization of B could not be completed and
129: * no eigenvalues or eigenvectors were computed.
130: *
131: * Further Details
132: * ===============
133: *
134: * Based on contributions by
135: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
136: *
137: * =====================================================================
138: *
139: * .. Parameters ..
140: DOUBLE PRECISION TWO
141: PARAMETER ( TWO = 2.0D+0 )
142: * ..
143: * .. Local Scalars ..
144: LOGICAL LQUERY, UPPER, WANTZ
145: CHARACTER TRANS
146: INTEGER J, LIWMIN, LWMIN, NEIG
147: * ..
148: * .. External Functions ..
149: LOGICAL LSAME
150: EXTERNAL LSAME
151: * ..
152: * .. External Subroutines ..
153: EXTERNAL DPPTRF, DSPEVD, DSPGST, DTPMV, DTPSV, XERBLA
154: * ..
155: * .. Intrinsic Functions ..
156: INTRINSIC DBLE, MAX
157: * ..
158: * .. Executable Statements ..
159: *
160: * Test the input parameters.
161: *
162: WANTZ = LSAME( JOBZ, 'V' )
163: UPPER = LSAME( UPLO, 'U' )
164: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
165: *
166: INFO = 0
167: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
168: INFO = -1
169: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
170: INFO = -2
171: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
172: INFO = -3
173: ELSE IF( N.LT.0 ) THEN
174: INFO = -4
175: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
176: INFO = -9
177: END IF
178: *
179: IF( INFO.EQ.0 ) THEN
180: IF( N.LE.1 ) THEN
181: LIWMIN = 1
182: LWMIN = 1
183: ELSE
184: IF( WANTZ ) THEN
185: LIWMIN = 3 + 5*N
186: LWMIN = 1 + 6*N + 2*N**2
187: ELSE
188: LIWMIN = 1
189: LWMIN = 2*N
190: END IF
191: END IF
192: WORK( 1 ) = LWMIN
193: IWORK( 1 ) = LIWMIN
194: *
195: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
196: INFO = -11
197: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
198: INFO = -13
199: END IF
200: END IF
201: *
202: IF( INFO.NE.0 ) THEN
203: CALL XERBLA( 'DSPGVD', -INFO )
204: RETURN
205: ELSE IF( LQUERY ) THEN
206: RETURN
207: END IF
208: *
209: * Quick return if possible
210: *
211: IF( N.EQ.0 )
212: $ RETURN
213: *
214: * Form a Cholesky factorization of BP.
215: *
216: CALL DPPTRF( UPLO, N, BP, INFO )
217: IF( INFO.NE.0 ) THEN
218: INFO = N + INFO
219: RETURN
220: END IF
221: *
222: * Transform problem to standard eigenvalue problem and solve.
223: *
224: CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
225: CALL DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
226: $ LIWORK, INFO )
227: LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) )
228: LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) )
229: *
230: IF( WANTZ ) THEN
231: *
232: * Backtransform eigenvectors to the original problem.
233: *
234: NEIG = N
235: IF( INFO.GT.0 )
236: $ NEIG = INFO - 1
237: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
238: *
239: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
240: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
241: *
242: IF( UPPER ) THEN
243: TRANS = 'N'
244: ELSE
245: TRANS = 'T'
246: END IF
247: *
248: DO 10 J = 1, NEIG
249: CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
250: $ 1 )
251: 10 CONTINUE
252: *
253: ELSE IF( ITYPE.EQ.3 ) THEN
254: *
255: * For B*A*x=(lambda)*x;
256: * backtransform eigenvectors: x = L*y or U'*y
257: *
258: IF( UPPER ) THEN
259: TRANS = 'T'
260: ELSE
261: TRANS = 'N'
262: END IF
263: *
264: DO 20 J = 1, NEIG
265: CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
266: $ 1 )
267: 20 CONTINUE
268: END IF
269: END IF
270: *
271: WORK( 1 ) = LWMIN
272: IWORK( 1 ) = LIWMIN
273: *
274: RETURN
275: *
276: * End of DSPGVD
277: *
278: END
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