1 SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
2 $ INFO )
3 *
4 * -- LAPACK driver routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
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)**T*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**T*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
2 $ INFO )
3 *
4 * -- LAPACK driver routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
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)**T*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**T*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