PDNEUPD(3) MathKeisan PARPACK routine PDNEUPD(3)
NAME
PDNEUPD - Postprocessing routine for large-scale non-symmetric eigen-
value calculation.
SYNOPSIS
SUBROUTINE PDNEUPD
( COMM, RVEC, HOWMNY, SELECT, DR, DI, Z, LDZ, SIGMAR, SIGMAI,
WORKEV, 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
DOUBLE PRECISION SIGMAR, SIGMAI, TOL
INTEGER IPARAM(11), IPNTR(14)
LOGICAL SELECT(NCV)
DOUBLE PRECISION DR(NEV+1) , DI(NEV+1) , RESID(N) ,
V(LDV,NCV) , Z(LDZ,*) , WORKD(3*N),
WORKL(LWORKL), WORKEV(3*NCV)
PURPOSE
PDNEUPD returns the converged approximations to eigenvalues
of A*z = lambda*B*z and (optionally):
(1) The corresponding approximate eigenvectors;
(2) An orthonormal basis for the associated approximate
invariant subspace;
(3) Both.
There is negligible additional cost to obtain eigenvectors. An orthonormal
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).
The approximate eigenvalues and eigenvectors of A*z = lambda*B*z
are derived from approximate eigenvalues and eigenvectors of
of the linear operator OP prescribed by the MODE selection in the
call to PDNAUPD . PDNAUPD 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
Schur basis.
See documentation in the header of the subroutine PDNAUPD for
definition of OP as well as other terms and the relation of computed
Ritz values and Ritz vectors of OP with respect to the given problem
A*z = lambda*B*z. For a brief description, see definitions of
IPARAM(7), MODE and WHICH in the documentation of PDNAUPD .
ARGUMENTS
COMM MPI Communicator for the processor grid. (INPUT)
RVEC LOGICAL (INPUT)
Specifies whether a basis for the invariant subspace corresponding
to the converged Ritz value approximations for the eigenproblem
A*z = lambda*B*z is computed.
RVEC = .FALSE. Compute Ritz values only.
RVEC = .TRUE. Compute the Ritz vectors or Schur vectors.
See Remarks below.
HOWMNY Character*1 (INPUT)
Specifies the form of the basis for the invariant subspace
corresponding to the converged Ritz values that is to be computed.
= 'A': Compute NEV Ritz vectors;
= 'P': Compute NEV Schur vectors;
= 'S': compute some of the Ritz vectors, specified
by the logical array SELECT.
SELECT Logical array of dimension NCV. (INPUT)
If HOWMNY = 'S', SELECT specifies the Ritz vectors to be
computed. To select the Ritz vector corresponding to a
Ritz value (DR(j), DI(j)), SELECT(j) must be set to .TRUE..
If HOWMNY = 'A' or 'P', SELECT is used as internal workspace.
DR Double precision array of dimension NEV+1. (OUTPUT)
If IPARAM(7) = 1,2 or 3 and SIGMAI=0.0 then on exit: DR contains
the real part of the Ritz approximations to the eigenvalues of
A*z = lambda*B*z.
If IPARAM(7) = 3, 4 and SIGMAI is not equal to zero, then on exit:
DR contains the real part of the Ritz values of OP computed by
PDNAUPD . A further computation must be performed by the user
to transform the Ritz values computed for OP by PDNAUPD to those
of the original system A*z = lambda*B*z. See remark 3 below.
DI Double precision array of dimension NEV+1. (OUTPUT)
On exit, DI contains the imaginary part of the Ritz value
approximations to the eigenvalues of A*z = lambda*B*z associated
with DR.
NOTE: When Ritz values are complex, they will come in complex
conjugate pairs. If eigenvectors are requested, the
corresponding Ritz vectors will also come in conjugate
pairs and the real and imaginary parts of these are
represented in two consecutive columns of the array Z
(see below).
Z Double precision N by NEV+1 array if RVEC = .TRUE. and HOWMNY = 'A'. (OUTPUT)
On exit, if RVEC = .TRUE. and HOWMNY = 'A', then the columns of
Z represent approximate eigenvectors (Ritz vectors) corresponding
to the NCONV=IPARAM(5) Ritz values for eigensystem
A*z = lambda*B*z.
The complex Ritz vector associated with the Ritz value
with positive imaginary part is stored in two consecutive
columns. The first column holds the real part of the Ritz
vector and the second column holds the imaginary part. The
Ritz vector associated with the Ritz value with negative
imaginary part is simply the complex conjugate of the Ritz vector
associated with the positive imaginary part.
If RVEC = .FALSE. or HOWMNY = 'P', then Z is not referenced.
NOTE: If if RVEC = .TRUE. and a Schur basis is not required,
the array Z may be set equal to first NEV+1 columns of the Arnoldi
basis array V computed by PDNAUPD . In this case the Arnoldi basis
will be destroyed and overwritten with the eigenvector basis.
LDZ Integer. (INPUT)
The leading dimension of the array Z. If Ritz vectors are
desired, then LDZ >= max( 1, N ). In any case, LDZ >= 1.
SIGMAR Double precision (INPUT)
If IPARAM(7) = 3 or 4, represents the real part of the shift.
Not referenced if IPARAM(7) = 1 or 2.
SIGMAI Double precision (INPUT)
If IPARAM(7) = 3 or 4, represents the imaginary part of the shift.
Not referenced if IPARAM(7) = 1 or 2. See remark 3 below.
WORKEV Double precision work array of dimension 3*NCV. (WORKSPACE)
**** The remaining arguments MUST be the same as for the ****
**** call to PDNAUPD 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 PDNEUPD following the last call
to PDNAUPD . These arguments MUST NOT BE MODIFIED between
the the last call to PDNAUPD and the call to PDNEUPD .
Three of these parameters (V, WORKL, INFO) are also output parameters:
V Double precision N by NCV array. (INPUT/OUTPUT)
Upon INPUT: the NCV columns of V contain the Arnoldi basis
vectors for OP as constructed by PDNAUPD .
Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns
contain approximate Schur vectors that span the
desired invariant subspace. See Remark 2 below.
NOTE: If the array Z has been set equal to first NEV+1 columns
of the array V and RVEC=.TRUE. and HOWMNY= 'A', then the
Arnoldi basis held by V has been overwritten by the desired
Ritz vectors. If a separate array Z has been passed then
the first NCONV=IPARAM(5) columns of V will contain approximate
Schur vectors that span the desired invariant subspace.
WORKL Double precision work array of length LWORKL. (OUTPUT/WORKSPACE)
WORKL(1:ncv*ncv+3*ncv) contains information obtained in
PDNAUPD . They are not changed by PDNEUPD .
WORKL(ncv*ncv+3*ncv+1:3*ncv*ncv+6*ncv) holds the
real and imaginary part of the untransformed Ritz values,
the upper quasi-triangular matrix for H, and the
associated matrix representation of the invariant subspace for H.
Note: IPNTR(9:13) contains the pointers into WORKL for addresses
of the above information computed by PDNEUPD .
-------------------------------------------------------------
IPNTR(9): pointer to the real part of the NCV RITZ values of the
original system.
IPNTR(10): pointer to the imaginary part of the NCV RITZ values of
the original system.
IPNTR(11): pointer to the NCV corresponding error bounds.
IPNTR(12): pointer to the NCV by NCV upper quasi-triangular
Schur matrix for H.
IPNTR(13): pointer to the NCV by NCV matrix of eigenvectors
of the upper Hessenberg matrix H. Only referenced by
PDNEUPD if RVEC = .TRUE. See Remark 2 below.
-------------------------------------------------------------
INFO Integer. (OUTPUT)
Error flag on output.
= 0: Normal exit.
= 1: The Schur form computed by LAPACK routine dlahqr
could not be reordered by LAPACK routine dtrsen .
Re-enter subroutine pdneupd with IPARAM(5)=NCV and
increase the size of the arrays DR and DI to have
dimension at least dimension NCV and allocate at least NCV
columns for Z. NOTE: Not necessary if Z and V share
the same space. Please notify the authors if this error
occurs.
= -1: N must be positive.
= -2: NEV must be positive.
= -3: NCV-NEV >= 2 and less than or equal to N.
= -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI'
= -6: BMAT must be one of 'I' or 'G'.
= -7: Length of private work WORKL array is not sufficient.
= -8: Error return from calculation of a real Schur form.
Informational error from LAPACK routine dlahqr .
= -9: Error return from calculation of eigenvectors.
Informational error from LAPACK routine dtrevc .
= -10: IPARAM(7) must be 1,2,3,4.
= -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible.
= -12: HOWMNY = 'S' not yet implemented
= -13: HOWMNY must be one of 'A' or 'P' if RVEC = .true.
= -14: PDNAUPD did not find any eigenvalues to sufficient
accuracy.
= -15: PDNEUPD got a different count of the number of converged
Ritz values than PDNAUPD got. This indicates the user
probably made an error in passing data from PDNAUPD to
PDNEUPD or that the data was modified before entering
PDNEUPD .
MathKeisan PDNEUPD(3)