1DSPGVD(1) LAPACK driver routine (version 3.2) DSPGVD(1)
2
6 DSPGVD - computes all the eigenvalues, and optionally, the eigenvectors
7 of a 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
31 floating point arithmetic. It will work on machines with a guard digit
32 in add/subtract, or on those binary machines without guard digits which
33 subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
34 conceivably fail on hexadecimal or decimal machines without guard dig‐
35 its, but we know of none.
36
38 ITYPE (input) INTEGER
39 Specifies the problem type to be solved:
40 = 1: A*x = (lambda)*B*x
41 = 2: A*B*x = (lambda)*x
42 = 3: B*A*x = (lambda)*x
43 JOBZ (input) CHARACTER*1
45 = 'N': Compute eigenvalues only;
46 = 'V': Compute eigenvalues and eigenvectors.
47 UPLO (input) CHARACTER*1
49 = 'U': Upper triangles of A and B are stored;
50 = 'L': Lower triangles of A and B are stored.
51 N (input) INTEGER
53 The order of the matrices A and B. N >= 0.
54 AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
56 On entry, the upper or lower triangle of the symmetric matrix
57 A, packed columnwise in a linear array. The j-th column of A
58 is stored in the array AP as follows: if UPLO = 'U', AP(i +
59 (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
60 (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, the contents
61 of AP are destroyed.
62 BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
64 On entry, the upper or lower triangle of the symmetric matrix
65 B, packed columnwise in a linear array. The j-th column of B
66 is stored in the array BP as follows: if UPLO = 'U', BP(i +
67 (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i +
68 (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. On exit, the triangular
69 factor U or L from the Cholesky factorization B = U**T*U or B =
70 L*L**T, in the same storage format as B.
71 W (output) DOUBLE PRECISION array, dimension (N)
73 If INFO = 0, the eigenvalues in ascending order.
74 Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
76 If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
77 eigenvectors. The eigenvectors are normalized as follows: if
78 ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I.
79 If JOBZ = 'N', then Z is not referenced.
80 LDZ (input) INTEGER
82 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
83 'V', LDZ >= max(1,N).
84 WORK (workspace/output) DOUBLE PRECISION array, dimension
86 (MAX(1,LWORK))
87 On exit, if INFO = 0, WORK(1) returns the required LWORK.
88 LWORK (input) INTEGER
90 The dimension of the array WORK. If N <= 1,
91 LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= 2*N. If JOBZ =
92 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. If LWORK = -1, then
93 a workspace query is assumed; the routine only calculates the
94 required sizes of the WORK and IWORK arrays, returns these val‐
95 ues as the first entries of the WORK and IWORK arrays, and no
96 error message related to LWORK or LIWORK is issued by XERBLA.
97 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
99 On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
100 LIWORK (input) INTEGER
102 The dimension of the array IWORK. If JOBZ = 'N' or N <= 1,
103 LIWORK >= 1. If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. If
104 LIWORK = -1, then a workspace query is assumed; the routine
105 only calculates the required sizes of the WORK and IWORK
106 arrays, returns these values as the first entries of the WORK
107 and IWORK arrays, and no error message related to LWORK or
108 LIWORK is issued by XERBLA.
109 INFO (output) INTEGER
111 = 0: successful exit
112 < 0: if INFO = -i, the i-th argument had an illegal value
113 > 0: DPPTRF or DSPEVD returned an error code:
114 <= N: if INFO = i, DSPEVD failed to converge; i off-diagonal
115 elements of an intermediate tridiagonal form did not converge
116 to zero; > N: if INFO = N + i, for 1 <= i <= N, then the
117 leading minor of order i of B is not positive definite. The
118 factorization of B could not be completed and no eigenvalues or
119 eigenvectors were computed.
120
122 Based on contributions by
123 Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
124 LAPACK driver routine (version 3.N2o)vember 2008 DSPGVD(1)