PSSEUPD(3) MathKeisan PARPACK routine PSSEUPD(3)
NAME
PSSEUPD - Postprocessing routine for large-scale symmetric eigenvalue
calculation.
SYNOPSIS
SUBROUTINE PSSEUPD
( COMM, RVEC, HOWMNY, SELECT, D, Z, LDZ, SIGMA, BMAT, N, WHICH, NEV, TOL,
RESID, NCV, V, LDV, IPARAM, IPNTR, WORKD, WORKL, LWORKL, INFO )
CHARACTER BMAT, HOWMNY, WHICH*2
LOGICAL RVEC
INTEGER INFO, LDZ, LDV, LWORKL, N, NCV, NEV
REAL SIGMA, TOL
INTEGER IPARAM(7), IPNTR(11)
LOGICAL SELECT(NCV)
REAL D(NEV), RESID(N), V(LDV,NCV), Z(LDZ, NEV),
WORKD(2*N), WORKL(LWORKL)
PURPOSE
PSSEUPD returns the converged approximations to eigenvalues
of A*z = lambda*B*z and (optionally):
(1) the corresponding approximate eigenvectors,
(2) an orthonormal (Lanczos) basis for the associated approximate
invariant subspace,
(3) Both.
There is negligible additional cost to obtain eigenvectors. An orthonormal
(Lanczos) basis is always computed. There is an additional storage cost
of n*nev if both are requested (in this case a separate array Z must be
supplied).
These quantities are obtained from the Lanczos factorization computed
by PSSAUPD for the linear operator OP prescribed by the MODE selection
(see IPARAM(7) in PSSAUPD documentation.) PSSAUPD must be called before
this routine is called. These approximate eigenvalues and vectors are
commonly called Ritz values and Ritz vectors respectively. They are
referred to as such in the comments that follow. The computed orthonormal
basis for the invariant subspace corresponding to these Ritz values is
referred to as a Lanczos basis.
See documentation in the header of the subroutine PSSAUPD for a definition
of OP as well as other terms and the relation of computed Ritz values
and vectors of OP with respect to the given problem A*z = lambda*B*z.
The approximate eigenvalues of the original problem are returned in
ascending algebraic order. The user may elect to call this routine
once for each desired Ritz vector and store it peripherally if desired.
There is also the option of computing a selected set of these vectors
with a single call.
ARGUMENTS
COMM MPI Communicator for the processor grid. (INPUT)
RVEC LOGICAL (INPUT)
Specifies whether Ritz vectors corresponding to the Ritz value
approximations to the eigenproblem A*z = lambda*B*z are computed.
RVEC = .FALSE. Compute Ritz values only.
RVEC = .TRUE. Compute Ritz vectors.
HOWMNY Character*1 (INPUT)
Specifies how many Ritz vectors are wanted and the form of Z
the matrix of Ritz vectors. See remark 1 below.
= 'A': compute NEV Ritz vectors;
= 'S': compute some of the Ritz vectors, specified
by the logical array SELECT.
SELECT Logical array of dimension NCV. (INPUT/WORKSPACE)
If HOWMNY = 'S', SELECT specifies the Ritz vectors to be
computed. To select the Ritz vector corresponding to a
Ritz value D(j), SELECT(j) must be set to .TRUE..
If HOWMNY = 'A' , SELECT is used as workspace.
D Real array of dimension NEV. (OUTPUT)
On exit, D contains the Ritz value approximations to the
eigenvalues of A*z = lambda*B*z. The values are returned
in ascending order. If IPARAM(7) = 3,4,5 then D represents
the Ritz values of OP computed by pssaupd transformed to
those of the original eigensystem A*z = lambda*B*z. If
IPARAM(7) = 1,2 then the Ritz values of OP are the same
as the those of A*z = lambda*B*z.
Z Real N by NEV array if HOWMNY = 'A'. (OUTPUT)
On exit, Z contains the B-orthonormal Ritz vectors of the
eigensystem A*z = lambda*B*z corresponding to the Ritz
value approximations.
If RVEC = .FALSE. then Z is not referenced.
NOTE: The array Z may be set equal to first NEV columns of the
Arnoldi/Lanczos basis array V computed by PSSAUPD.
LDZ Integer. (INPUT)
The leading dimension of the array Z. If Ritz vectors are
desired, then LDZ .ge. max( 1, N ). In any case, LDZ .ge. 1.
SIGMA Real (INPUT)
If IPARAM(7) = 3,4,5 represents the shift. Not referenced if
IPARAM(7) = 1 or 2.
**** The remaining arguments MUST be the same as for the ****
**** call to PSNAUPD that was just completed. ****
NOTE: The remaining arguments
BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, IPNTR,
WORKD, WORKL, LWORKL, INFO
must be passed directly to PSSEUPD following the last call
to PSSAUPD. These arguments MUST NOT BE MODIFIED between
the the last call to PSSAUPD and the call to PSSEUPD.
Two of these parameters (WORKL, INFO) are also output parameters:
WORKL Real work array of length LWORKL. (OUTPUT/WORKSPACE)
WORKL(1:4*ncv) contains information obtained in
PSSAUPD. They are not changed by PSSEUPD.
WORKL(4*ncv+1:ncv*ncv+8*ncv) holds the
untransformed Ritz values, the computed error estimates,
and the associated eigenvector matrix of H.
Note: IPNTR(8:10) contains the pointers into WORKL for addresses
of the above information computed by PSSEUPD.
-------------------------------------------------------------
IPNTR(8): pointer to the NCV RITZ values of the original system.
IPNTR(9): pointer to the NCV corresponding error bounds.
IPNTR(10): pointer to the NCV by NCV matrix of eigenvectors
of the tridiagonal matrix T. Only referenced by
PSSEUPD if RVEC = .TRUE. See Remarks.
-------------------------------------------------------------
INFO Integer. (OUTPUT)
Error flag on output.
= 0: Normal exit.
= -1: N must be positive.
= -2: NEV must be positive.
= -3: NCV must be greater than NEV and less than or equal to N.
= -5: WHICH must be one of 'LM', 'SM', 'LA', 'SA' or 'BE'.
= -6: BMAT must be one of 'I' or 'G'.
= -7: Length of private work WORKL array is not sufficient.
= -8: Error return from trid. eigenvalue calculation;
Information error from LAPACK routine ssteqr.
= -9: Starting vector is zero.
= -10: IPARAM(7) must be 1,2,3,4,5.
= -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible.
= -12: NEV and WHICH = 'BE' are incompatible.
= -14: PSSAUPD did not find any eigenvalues to sufficient
accuracy.
= -15: HOWMNY must be one of 'A' or 'S' if RVEC = .true.
= -16: HOWMNY = 'S' not yet implemented
= -17: SSEUPD got a different count of the number of converged
Ritz values than SSAUPD got. This indicates the user
probably made an error in passing data from SSAUPD to
SSEUPD or that the data was modified before entering
SSEUPD.
MathKeisan PSSEUPD(3)