Annotation of rpl/lapack/lapack/dspgv.f, revision 1.7
1.1 bertrand 1: SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
2: $ 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, N
12: * ..
13: * .. Array Arguments ..
14: DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
15: $ Z( LDZ, * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * DSPGV computes all the eigenvalues and, optionally, the eigenvectors
22: * of a real generalized symmetric-definite eigenproblem, of the form
23: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
24: * Here A and B are assumed to be symmetric, stored in packed format,
25: * and B is also positive definite.
26: *
27: * Arguments
28: * =========
29: *
30: * ITYPE (input) INTEGER
31: * Specifies the problem type to be solved:
32: * = 1: A*x = (lambda)*B*x
33: * = 2: A*B*x = (lambda)*x
34: * = 3: B*A*x = (lambda)*x
35: *
36: * JOBZ (input) CHARACTER*1
37: * = 'N': Compute eigenvalues only;
38: * = 'V': Compute eigenvalues and eigenvectors.
39: *
40: * UPLO (input) CHARACTER*1
41: * = 'U': Upper triangles of A and B are stored;
42: * = 'L': Lower triangles of A and B are stored.
43: *
44: * N (input) INTEGER
45: * The order of the matrices A and B. N >= 0.
46: *
47: * AP (input/output) DOUBLE PRECISION array, dimension
48: * (N*(N+1)/2)
49: * On entry, the upper or lower triangle of the symmetric matrix
50: * A, packed columnwise in a linear array. The j-th column of A
51: * is stored in the array AP as follows:
52: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
53: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
54: *
55: * On exit, the contents of AP are destroyed.
56: *
57: * BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
58: * On entry, the upper or lower triangle of the symmetric matrix
59: * B, packed columnwise in a linear array. The j-th column of B
60: * is stored in the array BP as follows:
61: * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
62: * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
63: *
64: * On exit, the triangular factor U or L from the Cholesky
65: * factorization B = U**T*U or B = L*L**T, in the same storage
66: * format as B.
67: *
68: * W (output) DOUBLE PRECISION array, dimension (N)
69: * If INFO = 0, the eigenvalues in ascending order.
70: *
71: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
72: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
73: * eigenvectors. The eigenvectors are normalized as follows:
74: * if ITYPE = 1 or 2, Z**T*B*Z = I;
75: * if ITYPE = 3, Z**T*inv(B)*Z = I.
76: * If JOBZ = 'N', then Z is not referenced.
77: *
78: * LDZ (input) INTEGER
79: * The leading dimension of the array Z. LDZ >= 1, and if
80: * JOBZ = 'V', LDZ >= max(1,N).
81: *
82: * WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
83: *
84: * INFO (output) INTEGER
85: * = 0: successful exit
86: * < 0: if INFO = -i, the i-th argument had an illegal value
87: * > 0: DPPTRF or DSPEV returned an error code:
88: * <= N: if INFO = i, DSPEV failed to converge;
89: * i off-diagonal elements of an intermediate
90: * tridiagonal form did not converge to zero.
91: * > N: if INFO = n + i, for 1 <= i <= n, then the leading
92: * minor of order i of B is not positive definite.
93: * The factorization of B could not be completed and
94: * no eigenvalues or eigenvectors were computed.
95: *
96: * =====================================================================
97: *
98: * .. Local Scalars ..
99: LOGICAL UPPER, WANTZ
100: CHARACTER TRANS
101: INTEGER J, NEIG
102: * ..
103: * .. External Functions ..
104: LOGICAL LSAME
105: EXTERNAL LSAME
106: * ..
107: * .. External Subroutines ..
108: EXTERNAL DPPTRF, DSPEV, DSPGST, DTPMV, DTPSV, XERBLA
109: * ..
110: * .. Executable Statements ..
111: *
112: * Test the input parameters.
113: *
114: WANTZ = LSAME( JOBZ, 'V' )
115: UPPER = LSAME( UPLO, 'U' )
116: *
117: INFO = 0
118: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
119: INFO = -1
120: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
121: INFO = -2
122: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
123: INFO = -3
124: ELSE IF( N.LT.0 ) THEN
125: INFO = -4
126: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
127: INFO = -9
128: END IF
129: IF( INFO.NE.0 ) THEN
130: CALL XERBLA( 'DSPGV ', -INFO )
131: RETURN
132: END IF
133: *
134: * Quick return if possible
135: *
136: IF( N.EQ.0 )
137: $ RETURN
138: *
139: * Form a Cholesky factorization of B.
140: *
141: CALL DPPTRF( UPLO, N, BP, INFO )
142: IF( INFO.NE.0 ) THEN
143: INFO = N + INFO
144: RETURN
145: END IF
146: *
147: * Transform problem to standard eigenvalue problem and solve.
148: *
149: CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
150: CALL DSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
151: *
152: IF( WANTZ ) THEN
153: *
154: * Backtransform eigenvectors to the original problem.
155: *
156: NEIG = N
157: IF( INFO.GT.0 )
158: $ NEIG = INFO - 1
159: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
160: *
161: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
162: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
163: *
164: IF( UPPER ) THEN
165: TRANS = 'N'
166: ELSE
167: TRANS = 'T'
168: END IF
169: *
170: DO 10 J = 1, NEIG
171: CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
172: $ 1 )
173: 10 CONTINUE
174: *
175: ELSE IF( ITYPE.EQ.3 ) THEN
176: *
177: * For B*A*x=(lambda)*x;
178: * backtransform eigenvectors: x = L*y or U'*y
179: *
180: IF( UPPER ) THEN
181: TRANS = 'T'
182: ELSE
183: TRANS = 'N'
184: END IF
185: *
186: DO 20 J = 1, NEIG
187: CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
188: $ 1 )
189: 20 CONTINUE
190: END IF
191: END IF
192: RETURN
193: *
194: * End of DSPGV
195: *
196: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dspgv.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack