sspgv (l) - Linux Manuals
sspgv: computes all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
Command to display sspgv manual in Linux: $ man l sspgv
NAME
SSPGV - computes all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
SYNOPSIS
- SUBROUTINE SSPGV(
-
ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
INFO )
-
CHARACTER
JOBZ, UPLO
-
INTEGER
INFO, ITYPE, LDZ, N
-
REAL
AP( * ), BP( * ), W( * ), WORK( * ),
Z( LDZ, * )
PURPOSE
SSPGV computes all the eigenvalues and, optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be symmetric, stored in packed format,
and B is also positive definite.
ARGUMENTS
- ITYPE (input) INTEGER
-
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
- JOBZ (input) CHARACTER*1
-
= aqNaq: Compute eigenvalues only;
= aqVaq: Compute eigenvalues and eigenvectors.
- UPLO (input) CHARACTER*1
-
= aqUaq: Upper triangles of A and B are stored;
= aqLaq: Lower triangles of A and B are stored.
- N (input) INTEGER
-
The order of the matrices A and B. N >= 0.
- AP (input/output) REAL array, dimension
-
(N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = aqUaq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = aqLaq, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, the contents of AP are destroyed.
- BP (input/output) REAL array, dimension (N*(N+1)/2)
-
On entry, the upper or lower triangle of the symmetric matrix
B, packed columnwise in a linear array. The j-th column of B
is stored in the array BP as follows:
if UPLO = aqUaq, BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = aqLaq, BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
On exit, the triangular factor U or L from the Cholesky
factorization B = U**T*U or B = L*L**T, in the same storage
format as B.
- W (output) REAL array, dimension (N)
-
If INFO = 0, the eigenvalues in ascending order.
- Z (output) REAL array, dimension (LDZ, N)
-
If JOBZ = aqVaq, then if INFO = 0, Z contains the matrix Z of
eigenvectors. The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.
If JOBZ = aqNaq, then Z is not referenced.
- LDZ (input) INTEGER
-
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = aqVaq, LDZ >= max(1,N).
- WORK (workspace) REAL array, dimension (3*N)
-
- INFO (output) INTEGER
-
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: SPPTRF or SSPEV returned an error code:
<= N: if INFO = i, SSPEV failed to converge;
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero.
> N: if INFO = n + i, for 1 <= i <= n, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.