1DSPGVD(1) LAPACK driver routine (version 3.1) DSPGVD(1)
2
6 DSPGVD - all the eigenvalues, and optionally, the eigenvectors of a
7 real generalized symmetric-definite eigenproblem, of the form
8 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
9
11 SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
12 LWORK, IWORK, LIWORK, INFO )
13 CHARACTER JOBZ, UPLO
15 INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
17 INTEGER IWORK( * )
19 DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ), Z(
21 LDZ, * )
22
24 DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
25 of a real generalized symmetric-definite eigenproblem, of the form
26 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B
27 are assumed to be symmetric, stored in packed format, and B is also
28 positive definite.
29 If eigenvectors are desired, it uses a divide and conquer algorithm.
30 The divide and conquer algorithm makes very mild assumptions about
32 floating point arithmetic. It will work on machines with a guard digit
33 in add/subtract, or on those binary machines without guard digits which
34 subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
35 conceivably fail on hexadecimal or decimal machines without guard dig‐
36 its, but we know of none.
37
40 ITYPE (input) INTEGER
41 Specifies the problem type to be solved:
42 = 1: A*x = (lambda)*B*x
43 = 2: A*B*x = (lambda)*x
44 = 3: B*A*x = (lambda)*x
45 JOBZ (input) CHARACTER*1
47 = 'N': Compute eigenvalues only;
48 = 'V': Compute eigenvalues and eigenvectors.
49 UPLO (input) CHARACTER*1
51 = 'U': Upper triangles of A and B are stored;
52 = 'L': Lower triangles of A and B are stored.
53 N (input) INTEGER
55 The order of the matrices A and B. N >= 0.
56 AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
58 On entry, the upper or lower triangle of the symmetric matrix
59 A, packed columnwise in a linear array. The j-th column of A
60 is stored in the array AP as follows: if UPLO = 'U', AP(i +
61 (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
62 (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
63 On exit, the contents of AP are destroyed.
65 BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
67 On entry, the upper or lower triangle of the symmetric matrix
68 B, packed columnwise in a linear array. The j-th column of B
69 is stored in the array BP as follows: if UPLO = 'U', BP(i +
70 (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i +
71 (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
72 On exit, the triangular factor U or L from the Cholesky factor‐
74 ization B = U**T*U or B = L*L**T, in the same storage format as
75 B.
76 W (output) DOUBLE PRECISION array, dimension (N)
78 If INFO = 0, the eigenvalues in ascending order.
79 Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
81 If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
82 eigenvectors. The eigenvectors are normalized as follows: if
83 ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I.
84 If JOBZ = 'N', then Z is not referenced.
85 LDZ (input) INTEGER
87 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
88 'V', LDZ >= max(1,N).
89 WORK (workspace/output) DOUBLE PRECISION array, dimension
91 (MAX(1,LWORK))
92 On exit, if INFO = 0, WORK(1) returns the required LWORK.
93 LWORK (input) INTEGER
95 The dimension of the array WORK. If N <= 1,
96 LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= 2*N. If JOBZ =
97 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
98 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 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
106 On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
107 LIWORK (input) INTEGER
109 The dimension of the array IWORK. If JOBZ = 'N' or N <= 1,
110 LIWORK >= 1. If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
111 If LIWORK = -1, then a workspace query is assumed; the routine
113 only calculates the required sizes of the WORK and IWORK
114 arrays, returns these values as the first entries of the WORK
115 and IWORK arrays, and no error message related to LWORK or
116 LIWORK is issued by XERBLA.
117 INFO (output) INTEGER
119 = 0: successful exit
120 < 0: if INFO = -i, the i-th argument had an illegal value
121 > 0: DPPTRF or DSPEVD returned an error code:
122 <= N: if INFO = i, DSPEVD failed to converge; i off-diagonal
123 elements of an intermediate tridiagonal form did not converge
124 to zero; > N: if INFO = N + i, for 1 <= i <= N, then the
125 leading minor of order i of B is not positive definite. The
126 factorization of B could not be completed and no eigenvalues or
127 eigenvectors were computed.
128
130 Based on contributions by
131 Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
132 LAPACK driver routine (version 3.N1o)vember 2006 DSPGVD(1)