1 SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
2 $ RWORK, 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 RWORK( * ), W( * )
15 COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * ZHPGV computes all the eigenvalues and, optionally, the eigenvectors
22 * of a complex generalized Hermitian-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 Hermitian, 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) COMPLEX*16 array, dimension (N*(N+1)/2)
48 * On entry, the upper or lower triangle of the Hermitian matrix
49 * A, packed columnwise in a linear array. The j-th column of A
50 * is stored in the array AP as follows:
51 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
52 * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
53 *
54 * On exit, the contents of AP are destroyed.
55 *
56 * BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
57 * On entry, the upper or lower triangle of the Hermitian matrix
58 * B, packed columnwise in a linear array. The j-th column of B
59 * is stored in the array BP as follows:
60 * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
61 * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
62 *
63 * On exit, the triangular factor U or L from the Cholesky
64 * factorization B = U**H*U or B = L*L**H, in the same storage
65 * format as B.
66 *
67 * W (output) DOUBLE PRECISION array, dimension (N)
68 * If INFO = 0, the eigenvalues in ascending order.
69 *
70 * Z (output) COMPLEX*16 array, dimension (LDZ, N)
71 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
72 * eigenvectors. The eigenvectors are normalized as follows:
73 * if ITYPE = 1 or 2, Z**H*B*Z = I;
74 * if ITYPE = 3, Z**H*inv(B)*Z = I.
75 * If JOBZ = 'N', then Z is not referenced.
76 *
77 * LDZ (input) INTEGER
78 * The leading dimension of the array Z. LDZ >= 1, and if
79 * JOBZ = 'V', LDZ >= max(1,N).
80 *
81 * WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1))
82 *
83 * RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
84 *
85 * INFO (output) INTEGER
86 * = 0: successful exit
87 * < 0: if INFO = -i, the i-th argument had an illegal value
88 * > 0: ZPPTRF or ZHPEV returned an error code:
89 * <= N: if INFO = i, ZHPEV failed to converge;
90 * i off-diagonal elements of an intermediate
91 * tridiagonal form did not convergeto zero;
92 * > N: if INFO = N + i, for 1 <= i <= n, then the leading
93 * minor of order i of B is not positive definite.
94 * The factorization of B could not be completed and
95 * no eigenvalues or eigenvectors were computed.
96 *
97 * =====================================================================
98 *
99 * .. Local Scalars ..
100 LOGICAL UPPER, WANTZ
101 CHARACTER TRANS
102 INTEGER J, NEIG
103 * ..
104 * .. External Functions ..
105 LOGICAL LSAME
106 EXTERNAL LSAME
107 * ..
108 * .. External Subroutines ..
109 EXTERNAL XERBLA, ZHPEV, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
110 * ..
111 * .. Executable Statements ..
112 *
113 * Test the input parameters.
114 *
115 WANTZ = LSAME( JOBZ, 'V' )
116 UPPER = LSAME( UPLO, 'U' )
117 *
118 INFO = 0
119 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
120 INFO = -1
121 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
122 INFO = -2
123 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
124 INFO = -3
125 ELSE IF( N.LT.0 ) THEN
126 INFO = -4
127 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
128 INFO = -9
129 END IF
130 IF( INFO.NE.0 ) THEN
131 CALL XERBLA( 'ZHPGV ', -INFO )
132 RETURN
133 END IF
134 *
135 * Quick return if possible
136 *
137 IF( N.EQ.0 )
138 $ RETURN
139 *
140 * Form a Cholesky factorization of B.
141 *
142 CALL ZPPTRF( UPLO, N, BP, INFO )
143 IF( INFO.NE.0 ) THEN
144 INFO = N + INFO
145 RETURN
146 END IF
147 *
148 * Transform problem to standard eigenvalue problem and solve.
149 *
150 CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
151 CALL ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO )
152 *
153 IF( WANTZ ) THEN
154 *
155 * Backtransform eigenvectors to the original problem.
156 *
157 NEIG = N
158 IF( INFO.GT.0 )
159 $ NEIG = INFO - 1
160 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
161 *
162 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
163 * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
164 *
165 IF( UPPER ) THEN
166 TRANS = 'N'
167 ELSE
168 TRANS = 'C'
169 END IF
170 *
171 DO 10 J = 1, NEIG
172 CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
173 $ 1 )
174 10 CONTINUE
175 *
176 ELSE IF( ITYPE.EQ.3 ) THEN
177 *
178 * For B*A*x=(lambda)*x;
179 * backtransform eigenvectors: x = L*y or U**H *y
180 *
181 IF( UPPER ) THEN
182 TRANS = 'C'
183 ELSE
184 TRANS = 'N'
185 END IF
186 *
187 DO 20 J = 1, NEIG
188 CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
189 $ 1 )
190 20 CONTINUE
191 END IF
192 END IF
193 RETURN
194 *
195 * End of ZHPGV
196 *
197 END
2 $ RWORK, 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 RWORK( * ), W( * )
15 COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * ZHPGV computes all the eigenvalues and, optionally, the eigenvectors
22 * of a complex generalized Hermitian-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 Hermitian, 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) COMPLEX*16 array, dimension (N*(N+1)/2)
48 * On entry, the upper or lower triangle of the Hermitian matrix
49 * A, packed columnwise in a linear array. The j-th column of A
50 * is stored in the array AP as follows:
51 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
52 * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
53 *
54 * On exit, the contents of AP are destroyed.
55 *
56 * BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
57 * On entry, the upper or lower triangle of the Hermitian matrix
58 * B, packed columnwise in a linear array. The j-th column of B
59 * is stored in the array BP as follows:
60 * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
61 * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
62 *
63 * On exit, the triangular factor U or L from the Cholesky
64 * factorization B = U**H*U or B = L*L**H, in the same storage
65 * format as B.
66 *
67 * W (output) DOUBLE PRECISION array, dimension (N)
68 * If INFO = 0, the eigenvalues in ascending order.
69 *
70 * Z (output) COMPLEX*16 array, dimension (LDZ, N)
71 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
72 * eigenvectors. The eigenvectors are normalized as follows:
73 * if ITYPE = 1 or 2, Z**H*B*Z = I;
74 * if ITYPE = 3, Z**H*inv(B)*Z = I.
75 * If JOBZ = 'N', then Z is not referenced.
76 *
77 * LDZ (input) INTEGER
78 * The leading dimension of the array Z. LDZ >= 1, and if
79 * JOBZ = 'V', LDZ >= max(1,N).
80 *
81 * WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1))
82 *
83 * RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
84 *
85 * INFO (output) INTEGER
86 * = 0: successful exit
87 * < 0: if INFO = -i, the i-th argument had an illegal value
88 * > 0: ZPPTRF or ZHPEV returned an error code:
89 * <= N: if INFO = i, ZHPEV failed to converge;
90 * i off-diagonal elements of an intermediate
91 * tridiagonal form did not convergeto zero;
92 * > N: if INFO = N + i, for 1 <= i <= n, then the leading
93 * minor of order i of B is not positive definite.
94 * The factorization of B could not be completed and
95 * no eigenvalues or eigenvectors were computed.
96 *
97 * =====================================================================
98 *
99 * .. Local Scalars ..
100 LOGICAL UPPER, WANTZ
101 CHARACTER TRANS
102 INTEGER J, NEIG
103 * ..
104 * .. External Functions ..
105 LOGICAL LSAME
106 EXTERNAL LSAME
107 * ..
108 * .. External Subroutines ..
109 EXTERNAL XERBLA, ZHPEV, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
110 * ..
111 * .. Executable Statements ..
112 *
113 * Test the input parameters.
114 *
115 WANTZ = LSAME( JOBZ, 'V' )
116 UPPER = LSAME( UPLO, 'U' )
117 *
118 INFO = 0
119 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
120 INFO = -1
121 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
122 INFO = -2
123 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
124 INFO = -3
125 ELSE IF( N.LT.0 ) THEN
126 INFO = -4
127 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
128 INFO = -9
129 END IF
130 IF( INFO.NE.0 ) THEN
131 CALL XERBLA( 'ZHPGV ', -INFO )
132 RETURN
133 END IF
134 *
135 * Quick return if possible
136 *
137 IF( N.EQ.0 )
138 $ RETURN
139 *
140 * Form a Cholesky factorization of B.
141 *
142 CALL ZPPTRF( UPLO, N, BP, INFO )
143 IF( INFO.NE.0 ) THEN
144 INFO = N + INFO
145 RETURN
146 END IF
147 *
148 * Transform problem to standard eigenvalue problem and solve.
149 *
150 CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
151 CALL ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO )
152 *
153 IF( WANTZ ) THEN
154 *
155 * Backtransform eigenvectors to the original problem.
156 *
157 NEIG = N
158 IF( INFO.GT.0 )
159 $ NEIG = INFO - 1
160 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
161 *
162 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
163 * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
164 *
165 IF( UPPER ) THEN
166 TRANS = 'N'
167 ELSE
168 TRANS = 'C'
169 END IF
170 *
171 DO 10 J = 1, NEIG
172 CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
173 $ 1 )
174 10 CONTINUE
175 *
176 ELSE IF( ITYPE.EQ.3 ) THEN
177 *
178 * For B*A*x=(lambda)*x;
179 * backtransform eigenvectors: x = L*y or U**H *y
180 *
181 IF( UPPER ) THEN
182 TRANS = 'C'
183 ELSE
184 TRANS = 'N'
185 END IF
186 *
187 DO 20 J = 1, NEIG
188 CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
189 $ 1 )
190 20 CONTINUE
191 END IF
192 END IF
193 RETURN
194 *
195 * End of ZHPGV
196 *
197 END