dspgvd.f(3) LAPACK dspgvd.f(3)
NAME
dspgvd.f -
SYNOPSIS
Functions/Subroutines
subroutine dspgvd (ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)
DSPGST
Function/Subroutine Documentation
subroutine dspgvd (integerITYPE, characterJOBZ, characterUPLO, integerN, double precision, dimension( * )AP, double precision, dimension( *
)BP, double precision, dimension( * )W, double precision, dimension( ldz, * )Z, integerLDZ, double precision, dimension( * )WORK,
integerLWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)
DSPGST
Purpose:
DSPGVD 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.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Parameters:
ITYPE
ITYPE is 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
JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N
N is INTEGER
The order of the matrices A and B. N >= 0.
AP
AP is DOUBLE PRECISION 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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, the contents of AP are destroyed.
BP
BP is DOUBLE PRECISION 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 = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = 'L', 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
W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z
Z is DOUBLE PRECISION array, dimension (LDZ, N)
If JOBZ = 'V', 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 = 'N', then Z is not referenced.
LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the required LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = 'N' and N > 1, LWORK >= 2*N.
If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the required sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK or
LIWORK is issued by XERBLA.
IWORK
IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
LIWORK
LIWORK is INTEGER
The dimension of the array IWORK.
If JOBZ = 'N' or N <= 1, LIWORK >= 1.
If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the required sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK or LIWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: DPPTRF or DSPEVD returned an error code:
<= N: if INFO = i, DSPEVD 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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Contributors:
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Definition at line 210 of file dspgvd.f.
Author
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Version 3.4.2 Tue Sep 25 2012 dspgvd.f(3)