.TH SSPGV 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) "
.SH NAME
SSPGV - 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
.SH SYNOPSIS
.TP 18
SUBROUTINE SSPGV(
ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
INFO )
.TP 18
.ti +4
CHARACTER
JOBZ, UPLO
.TP 18
.ti +4
INTEGER
INFO, ITYPE, LDZ, N
.TP 18
.ti +4
REAL
AP( * ), BP( * ), W( * ), WORK( * ),
Z( LDZ, * )
.SH 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.
.br
.SH ARGUMENTS
.TP 8
ITYPE (input) INTEGER
Specifies the problem type to be solved:
.br
= 1: A*x = (lambda)*B*x
.br
= 2: A*B*x = (lambda)*x
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= 3: B*A*x = (lambda)*x
.TP 8
JOBZ (input) CHARACTER*1
.br
= \(aqN\(aq: Compute eigenvalues only;
.br
= \(aqV\(aq: Compute eigenvalues and eigenvectors.
.TP 8
UPLO (input) CHARACTER*1
.br
= \(aqU\(aq: Upper triangles of A and B are stored;
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= \(aqL\(aq: Lower triangles of A and B are stored.
.TP 8
N (input) INTEGER
The order of the matrices A and B. N >= 0.
.TP 8
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 = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = \(aqL\(aq, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, the contents of AP are destroyed.
.TP 8
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 = \(aqU\(aq, BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = \(aqL\(aq, 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.
.TP 8
W (output) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
.TP 8
Z (output) REAL array, dimension (LDZ, N)
If JOBZ = \(aqV\(aq, 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 = \(aqN\(aq, then Z is not referenced.
.TP 8
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = \(aqV\(aq, LDZ >= max(1,N).
.TP 8
WORK (workspace) REAL array, dimension (3*N)
.TP 8
INFO (output) INTEGER
= 0: successful exit
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< 0: if INFO = -i, the i-th argument had an illegal value
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> 0: SPPTRF or SSPEV returned an error code:
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<= 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.