1SSPGV(1) LAPACK driver routine (version 3.1) SSPGV(1)
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6 SSPGV - all the eigenvalues and, optionally, the eigenvectors of a real
7 generalized symmetric-definite eigenproblem, of the form
8 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
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11 SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO )
12 CHARACTER JOBZ, UPLO
14 INTEGER INFO, ITYPE, LDZ, N
16 REAL AP( * ), BP( * ), W( * ), WORK( * ), Z( LDZ, * )
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20 SSPGV computes all the eigenvalues and, optionally, the eigenvectors of
21 a real generalized symmetric-definite eigenproblem, of the form
22 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B
23 are assumed to be symmetric, stored in packed format, and B is also
24 positive definite.
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28 ITYPE (input) INTEGER
29 Specifies the problem type to be solved:
30 = 1: A*x = (lambda)*B*x
31 = 2: A*B*x = (lambda)*x
32 = 3: B*A*x = (lambda)*x
33 JOBZ (input) CHARACTER*1
35 = 'N': Compute eigenvalues only;
36 = 'V': Compute eigenvalues and eigenvectors.
37 UPLO (input) CHARACTER*1
39 = 'U': Upper triangles of A and B are stored;
40 = 'L': Lower triangles of A and B are stored.
41 N (input) INTEGER
43 The order of the matrices A and B. N >= 0.
44 AP (input/output) REAL array, dimension
46 (N*(N+1)/2) On entry, the upper or lower triangle of the sym‐
47 metric matrix A, packed columnwise in a linear array. The j-th
48 column of A is stored in the array AP as follows: if UPLO =
49 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L',
50 AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
51 On exit, the contents of AP are destroyed.
53 BP (input/output) REAL array, dimension (N*(N+1)/2)
55 On entry, the upper or lower triangle of the symmetric matrix
56 B, packed columnwise in a linear array. The j-th column of B
57 is stored in the array BP as follows: if UPLO = 'U', BP(i +
58 (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i +
59 (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
60 On exit, the triangular factor U or L from the Cholesky factor‐
62 ization B = U**T*U or B = L*L**T, in the same storage format as
63 B.
64 W (output) REAL array, dimension (N)
66 If INFO = 0, the eigenvalues in ascending order.
67 Z (output) REAL array, dimension (LDZ, N)
69 If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
70 eigenvectors. The eigenvectors are normalized as follows: if
71 ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I.
72 If JOBZ = 'N', then Z is not referenced.
73 LDZ (input) INTEGER
75 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
76 'V', LDZ >= max(1,N).
77 WORK (workspace) REAL array, dimension (3*N)
79 INFO (output) INTEGER
81 = 0: successful exit
82 < 0: if INFO = -i, the i-th argument had an illegal value
83 > 0: SPPTRF or SSPEV returned an error code:
84 <= N: if INFO = i, SSPEV failed to converge; i off-diagonal
85 elements of an intermediate tridiagonal form did not converge
86 to zero. > N: if INFO = n + i, for 1 <= i <= n, then the
87 leading minor of order i of B is not positive definite. The
88 factorization of B could not be completed and no eigenvalues or
89 eigenvectors were computed.
90 LAPACK driver routine (version 3.N1o)vember 2006 SSPGV(1)