694 lines
29 KiB
Fortran
694 lines
29 KiB
Fortran
c\BeginDoc
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c
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c\Name: snaupd
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c
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c\Description:
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c Reverse communication interface for the Implicitly Restarted Arnoldi
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c iteration. This subroutine computes approximations to a few eigenpairs
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c of a linear operator "OP" with respect to a semi-inner product defined by
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c a symmetric positive semi-definite real matrix B. B may be the identity
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c matrix. NOTE: If the linear operator "OP" is real and symmetric
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c with respect to the real positive semi-definite symmetric matrix B,
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c i.e. B*OP = (OP`)*B, then subroutine ssaupd should be used instead.
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c
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c The computed approximate eigenvalues are called Ritz values and
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c the corresponding approximate eigenvectors are called Ritz vectors.
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c
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c snaupd is usually called iteratively to solve one of the
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c following problems:
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c
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c Mode 1: A*x = lambda*x.
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c ===> OP = A and B = I.
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c
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c Mode 2: A*x = lambda*M*x, M symmetric positive definite
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c ===> OP = inv[M]*A and B = M.
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c ===> (If M can be factored see remark 3 below)
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c
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c Mode 3: A*x = lambda*M*x, M symmetric semi-definite
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c ===> OP = Real_Part{ inv[A - sigma*M]*M } and B = M.
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c ===> shift-and-invert mode (in real arithmetic)
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c If OP*x = amu*x, then
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c amu = 1/2 * [ 1/(lambda-sigma) + 1/(lambda-conjg(sigma)) ].
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c Note: If sigma is real, i.e. imaginary part of sigma is zero;
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c Real_Part{ inv[A - sigma*M]*M } == inv[A - sigma*M]*M
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c amu == 1/(lambda-sigma).
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c
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c Mode 4: A*x = lambda*M*x, M symmetric semi-definite
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c ===> OP = Imaginary_Part{ inv[A - sigma*M]*M } and B = M.
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c ===> shift-and-invert mode (in real arithmetic)
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c If OP*x = amu*x, then
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c amu = 1/2i * [ 1/(lambda-sigma) - 1/(lambda-conjg(sigma)) ].
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c
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c Both mode 3 and 4 give the same enhancement to eigenvalues close to
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c the (complex) shift sigma. However, as lambda goes to infinity,
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c the operator OP in mode 4 dampens the eigenvalues more strongly than
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c does OP defined in mode 3.
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c
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c NOTE: The action of w <- inv[A - sigma*M]*v or w <- inv[M]*v
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c should be accomplished either by a direct method
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c using a sparse matrix factorization and solving
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c
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c [A - sigma*M]*w = v or M*w = v,
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c
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c or through an iterative method for solving these
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c systems. If an iterative method is used, the
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c convergence test must be more stringent than
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c the accuracy requirements for the eigenvalue
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c approximations.
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c
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c\Usage:
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c call snaupd
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c ( IDO, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM,
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c IPNTR, WORKD, WORKL, LWORKL, INFO )
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c
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c\Arguments
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c IDO Integer. (INPUT/OUTPUT)
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c Reverse communication flag. IDO must be zero on the first
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c call to snaupd. IDO will be set internally to
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c indicate the type of operation to be performed. Control is
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c then given back to the calling routine which has the
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c responsibility to carry out the requested operation and call
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c snaupd with the result. The operand is given in
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c WORKD(IPNTR(1)), the result must be put in WORKD(IPNTR(2)).
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c -------------------------------------------------------------
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c IDO = 0: first call to the reverse communication interface
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c IDO = -1: compute Y = OP * X where
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c IPNTR(1) is the pointer into WORKD for X,
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c IPNTR(2) is the pointer into WORKD for Y.
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c This is for the initialization phase to force the
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c starting vector into the range of OP.
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c IDO = 1: compute Y = OP * X where
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c IPNTR(1) is the pointer into WORKD for X,
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c IPNTR(2) is the pointer into WORKD for Y.
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c In mode 3 and 4, the vector B * X is already
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c available in WORKD(ipntr(3)). It does not
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c need to be recomputed in forming OP * X.
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c IDO = 2: compute Y = B * X where
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c IPNTR(1) is the pointer into WORKD for X,
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c IPNTR(2) is the pointer into WORKD for Y.
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c IDO = 3: compute the IPARAM(8) real and imaginary parts
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c of the shifts where INPTR(14) is the pointer
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c into WORKL for placing the shifts. See Remark
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c 5 below.
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c IDO = 99: done
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c -------------------------------------------------------------
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c
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c BMAT Character*1. (INPUT)
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c BMAT specifies the type of the matrix B that defines the
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c semi-inner product for the operator OP.
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c BMAT = 'I' -> standard eigenvalue problem A*x = lambda*x
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c BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*B*x
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c
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c N Integer. (INPUT)
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c Dimension of the eigenproblem.
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c
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c WHICH Character*2. (INPUT)
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c 'LM' -> want the NEV eigenvalues of largest magnitude.
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c 'SM' -> want the NEV eigenvalues of smallest magnitude.
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c 'LR' -> want the NEV eigenvalues of largest real part.
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c 'SR' -> want the NEV eigenvalues of smallest real part.
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c 'LI' -> want the NEV eigenvalues of largest imaginary part.
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c 'SI' -> want the NEV eigenvalues of smallest imaginary part.
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c
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c NEV Integer. (INPUT/OUTPUT)
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c Number of eigenvalues of OP to be computed. 0 < NEV < N-1.
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c
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c TOL Real scalar. (INPUT)
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c Stopping criterion: the relative accuracy of the Ritz value
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c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I))
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c where ABS(RITZ(I)) is the magnitude when RITZ(I) is complex.
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c DEFAULT = SLAMCH('EPS') (machine precision as computed
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c by the LAPACK auxiliary subroutine SLAMCH).
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c
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c RESID Real array of length N. (INPUT/OUTPUT)
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c On INPUT:
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c If INFO .EQ. 0, a random initial residual vector is used.
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c If INFO .NE. 0, RESID contains the initial residual vector,
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c possibly from a previous run.
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c On OUTPUT:
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c RESID contains the final residual vector.
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c
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c NCV Integer. (INPUT)
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c Number of columns of the matrix V. NCV must satisfy the two
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c inequalities 2 <= NCV-NEV and NCV <= N.
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c This will indicate how many Arnoldi vectors are generated
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c at each iteration. After the startup phase in which NEV
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c Arnoldi vectors are generated, the algorithm generates
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c approximately NCV-NEV Arnoldi vectors at each subsequent update
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c iteration. Most of the cost in generating each Arnoldi vector is
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c in the matrix-vector operation OP*x.
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c NOTE: 2 <= NCV-NEV in order that complex conjugate pairs of Ritz
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c values are kept together. (See remark 4 below)
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c
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c V Real array N by NCV. (OUTPUT)
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c Contains the final set of Arnoldi basis vectors.
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c
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c LDV Integer. (INPUT)
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c Leading dimension of V exactly as declared in the calling program.
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c
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c IPARAM Integer array of length 11. (INPUT/OUTPUT)
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c IPARAM(1) = ISHIFT: method for selecting the implicit shifts.
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c The shifts selected at each iteration are used to restart
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c the Arnoldi iteration in an implicit fashion.
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c -------------------------------------------------------------
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c ISHIFT = 0: the shifts are provided by the user via
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c reverse communication. The real and imaginary
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c parts of the NCV eigenvalues of the Hessenberg
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c matrix H are returned in the part of the WORKL
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c array corresponding to RITZR and RITZI. See remark
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c 5 below.
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c ISHIFT = 1: exact shifts with respect to the current
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c Hessenberg matrix H. This is equivalent to
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c restarting the iteration with a starting vector
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c that is a linear combination of approximate Schur
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c vectors associated with the "wanted" Ritz values.
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c -------------------------------------------------------------
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c
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c IPARAM(2) = No longer referenced.
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c
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c IPARAM(3) = MXITER
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c On INPUT: maximum number of Arnoldi update iterations allowed.
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c On OUTPUT: actual number of Arnoldi update iterations taken.
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c
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c IPARAM(4) = NB: blocksize to be used in the recurrence.
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c The code currently works only for NB = 1.
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c
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c IPARAM(5) = NCONV: number of "converged" Ritz values.
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c This represents the number of Ritz values that satisfy
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c the convergence criterion.
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c
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c IPARAM(6) = IUPD
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c No longer referenced. Implicit restarting is ALWAYS used.
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c
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c IPARAM(7) = MODE
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c On INPUT determines what type of eigenproblem is being solved.
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c Must be 1,2,3,4; See under \Description of snaupd for the
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c four modes available.
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c
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c IPARAM(8) = NP
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c When ido = 3 and the user provides shifts through reverse
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c communication (IPARAM(1)=0), snaupd returns NP, the number
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c of shifts the user is to provide. 0 < NP <=NCV-NEV. See Remark
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c 5 below.
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c
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c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO,
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c OUTPUT: NUMOP = total number of OP*x operations,
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c NUMOPB = total number of B*x operations if BMAT='G',
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c NUMREO = total number of steps of re-orthogonalization.
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c
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c IPNTR Integer array of length 14. (OUTPUT)
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c Pointer to mark the starting locations in the WORKD and WORKL
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c arrays for matrices/vectors used by the Arnoldi iteration.
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c -------------------------------------------------------------
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c IPNTR(1): pointer to the current operand vector X in WORKD.
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c IPNTR(2): pointer to the current result vector Y in WORKD.
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c IPNTR(3): pointer to the vector B * X in WORKD when used in
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c the shift-and-invert mode.
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c IPNTR(4): pointer to the next available location in WORKL
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c that is untouched by the program.
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c IPNTR(5): pointer to the NCV by NCV upper Hessenberg matrix
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c H in WORKL.
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c IPNTR(6): pointer to the real part of the ritz value array
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c RITZR in WORKL.
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c IPNTR(7): pointer to the imaginary part of the ritz value array
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c RITZI in WORKL.
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c IPNTR(8): pointer to the Ritz estimates in array WORKL associated
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c with the Ritz values located in RITZR and RITZI in WORKL.
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c
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c IPNTR(14): pointer to the NP shifts in WORKL. See Remark 5 below.
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c
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c Note: IPNTR(9:13) is only referenced by sneupd. See Remark 2 below.
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c
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c IPNTR(9): pointer to the real part of the NCV RITZ values of the
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c original system.
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c IPNTR(10): pointer to the imaginary part of the NCV RITZ values of
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c the original system.
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c IPNTR(11): pointer to the NCV corresponding error bounds.
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c IPNTR(12): pointer to the NCV by NCV upper quasi-triangular
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c Schur matrix for H.
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c IPNTR(13): pointer to the NCV by NCV matrix of eigenvectors
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c of the upper Hessenberg matrix H. Only referenced by
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c sneupd if RVEC = .TRUE. See Remark 2 below.
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c -------------------------------------------------------------
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c
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c WORKD Real work array of length 3*N. (REVERSE COMMUNICATION)
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c Distributed array to be used in the basic Arnoldi iteration
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c for reverse communication. The user should not use WORKD
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c as temporary workspace during the iteration. Upon termination
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c WORKD(1:N) contains B*RESID(1:N). If an invariant subspace
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c associated with the converged Ritz values is desired, see remark
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c 2 below, subroutine sneupd uses this output.
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c See Data Distribution Note below.
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c
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c WORKL Real work array of length LWORKL. (OUTPUT/WORKSPACE)
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c Private (replicated) array on each PE or array allocated on
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c the front end. See Data Distribution Note below.
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c
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c LWORKL Integer. (INPUT)
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c LWORKL must be at least 3*NCV**2 + 6*NCV.
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c
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c INFO Integer. (INPUT/OUTPUT)
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c If INFO .EQ. 0, a randomly initial residual vector is used.
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c If INFO .NE. 0, RESID contains the initial residual vector,
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c possibly from a previous run.
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c Error flag on output.
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c = 0: Normal exit.
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c = 1: Maximum number of iterations taken.
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c All possible eigenvalues of OP has been found. IPARAM(5)
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c returns the number of wanted converged Ritz values.
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c = 2: No longer an informational error. Deprecated starting
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c with release 2 of ARPACK.
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c = 3: No shifts could be applied during a cycle of the
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c Implicitly restarted Arnoldi iteration. One possibility
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c is to increase the size of NCV relative to NEV.
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c See remark 4 below.
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c = -1: N must be positive.
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c = -2: NEV must be positive.
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c = -3: NCV-NEV >= 2 and less than or equal to N.
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c = -4: The maximum number of Arnoldi update iteration
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c must be greater than zero.
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c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI'
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c = -6: BMAT must be one of 'I' or 'G'.
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c = -7: Length of private work array is not sufficient.
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c = -8: Error return from LAPACK eigenvalue calculation;
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c = -9: Starting vector is zero.
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c = -10: IPARAM(7) must be 1,2,3,4.
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c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatable.
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c = -12: IPARAM(1) must be equal to 0 or 1.
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c = -9999: Could not build an Arnoldi factorization.
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c IPARAM(5) returns the size of the current Arnoldi
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c factorization.
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c
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c\Remarks
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c 1. The computed Ritz values are approximate eigenvalues of OP. The
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c selection of WHICH should be made with this in mind when
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c Mode = 3 and 4. After convergence, approximate eigenvalues of the
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c original problem may be obtained with the ARPACK subroutine sneupd.
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c
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c 2. If a basis for the invariant subspace corresponding to the converged Ritz
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c values is needed, the user must call sneupd immediately following
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c completion of snaupd. This is new starting with release 2 of ARPACK.
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c
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c 3. If M can be factored into a Cholesky factorization M = LL`
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c then Mode = 2 should not be selected. Instead one should use
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c Mode = 1 with OP = inv(L)*A*inv(L`). Appropriate triangular
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c linear systems should be solved with L and L` rather
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c than computing inverses. After convergence, an approximate
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c eigenvector z of the original problem is recovered by solving
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c L`z = x where x is a Ritz vector of OP.
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c
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c 4. At present there is no a-priori analysis to guide the selection
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c of NCV relative to NEV. The only formal requrement is that NCV > NEV + 2.
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c However, it is recommended that NCV .ge. 2*NEV+1. If many problems of
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c the same type are to be solved, one should experiment with increasing
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c NCV while keeping NEV fixed for a given test problem. This will
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c usually decrease the required number of OP*x operations but it
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c also increases the work and storage required to maintain the orthogonal
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c basis vectors. The optimal "cross-over" with respect to CPU time
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c is problem dependent and must be determined empirically.
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c See Chapter 8 of Reference 2 for further information.
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c
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c 5. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the
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c NP = IPARAM(8) real and imaginary parts of the shifts in locations
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c real part imaginary part
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c ----------------------- --------------
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c 1 WORKL(IPNTR(14)) WORKL(IPNTR(14)+NP)
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c 2 WORKL(IPNTR(14)+1) WORKL(IPNTR(14)+NP+1)
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c . .
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c . .
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c . .
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c NP WORKL(IPNTR(14)+NP-1) WORKL(IPNTR(14)+2*NP-1).
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c
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c Only complex conjugate pairs of shifts may be applied and the pairs
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c must be placed in consecutive locations. The real part of the
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c eigenvalues of the current upper Hessenberg matrix are located in
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c WORKL(IPNTR(6)) through WORKL(IPNTR(6)+NCV-1) and the imaginary part
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c in WORKL(IPNTR(7)) through WORKL(IPNTR(7)+NCV-1). They are ordered
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c according to the order defined by WHICH. The complex conjugate
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c pairs are kept together and the associated Ritz estimates are located in
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c WORKL(IPNTR(8)), WORKL(IPNTR(8)+1), ... , WORKL(IPNTR(8)+NCV-1).
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c
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c-----------------------------------------------------------------------
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c
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c\Data Distribution Note:
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c
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c Fortran-D syntax:
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c ================
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c Real resid(n), v(ldv,ncv), workd(3*n), workl(lworkl)
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c decompose d1(n), d2(n,ncv)
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c align resid(i) with d1(i)
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c align v(i,j) with d2(i,j)
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c align workd(i) with d1(i) range (1:n)
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c align workd(i) with d1(i-n) range (n+1:2*n)
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c align workd(i) with d1(i-2*n) range (2*n+1:3*n)
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c distribute d1(block), d2(block,:)
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c replicated workl(lworkl)
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c
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c Cray MPP syntax:
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c ===============
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c Real resid(n), v(ldv,ncv), workd(n,3), workl(lworkl)
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c shared resid(block), v(block,:), workd(block,:)
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c replicated workl(lworkl)
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c
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c CM2/CM5 syntax:
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c ==============
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c
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c-----------------------------------------------------------------------
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c
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c include 'ex-nonsym.doc'
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c
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c-----------------------------------------------------------------------
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c
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c\BeginLib
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c
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c\Local variables:
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c xxxxxx real
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c
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c\References:
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c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in
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c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992),
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c pp 357-385.
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c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
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c Restarted Arnoldi Iteration", Rice University Technical Report
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c TR95-13, Department of Computational and Applied Mathematics.
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c 3. B.N. Parlett & Y. Saad, "Complex Shift and Invert Strategies for
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c Real Matrices", Linear Algebra and its Applications, vol 88/89,
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c pp 575-595, (1987).
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c
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c\Routines called:
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c snaup2 ARPACK routine that implements the Implicitly Restarted
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c Arnoldi Iteration.
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c ivout ARPACK utility routine that prints integers.
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c second ARPACK utility routine for timing.
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c svout ARPACK utility routine that prints vectors.
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c slamch LAPACK routine that determines machine constants.
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c
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c\Author
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c Danny Sorensen Phuong Vu
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c Richard Lehoucq CRPC / Rice University
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c Dept. of Computational & Houston, Texas
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c Applied Mathematics
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c Rice University
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c Houston, Texas
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c
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c\Revision history:
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c 12/16/93: Version '1.1'
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c
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c\SCCS Information: @(#)
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c FILE: naupd.F SID: 2.10 DATE OF SID: 08/23/02 RELEASE: 2
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c
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c\Remarks
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c
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c\EndLib
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c
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c-----------------------------------------------------------------------
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c
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subroutine snaupd
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& ( ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam,
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& ipntr, workd, workl, lworkl, info )
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c
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c %----------------------------------------------------%
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c | Include files for debugging and timing information |
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c %----------------------------------------------------%
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c
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include 'debug.h'
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include 'stat.h'
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c
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c %------------------%
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c | Scalar Arguments |
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c %------------------%
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c
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character bmat*1, which*2
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integer ido, info, ldv, lworkl, n, ncv, nev
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Real
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& tol
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c
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c %-----------------%
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c | Array Arguments |
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c %-----------------%
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c
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integer iparam(11), ipntr(14)
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Real
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& resid(n), v(ldv,ncv), workd(3*n), workl(lworkl)
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c
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c %------------%
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c | Parameters |
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c %------------%
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c
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Real
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& one, zero
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parameter (one = 1.0E+0, zero = 0.0E+0)
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c
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c %---------------%
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c | Local Scalars |
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c %---------------%
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c
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integer bounds, ierr, ih, iq, ishift, iupd, iw,
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& ldh, ldq, levec, mode, msglvl, mxiter, nb,
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& nev0, next, np, ritzi, ritzr, j
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save bounds, ih, iq, ishift, iupd, iw, ldh, ldq,
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& levec, mode, msglvl, mxiter, nb, nev0, next,
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& np, ritzi, ritzr
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c
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c %----------------------%
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c | External Subroutines |
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c %----------------------%
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c
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external snaup2, svout, ivout, second, sstatn
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c
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c %--------------------%
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c | External Functions |
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c %--------------------%
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c
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Real
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& slamch
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external slamch
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c
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c %-----------------------%
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c | Executable Statements |
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c %-----------------------%
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c
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if (ido .eq. 0) then
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c
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c %-------------------------------%
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c | Initialize timing statistics |
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c | & message level for debugging |
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c %-------------------------------%
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c
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call sstatn
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call second (t0)
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msglvl = mnaupd
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c
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c %----------------%
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c | Error checking |
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c %----------------%
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c
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ierr = 0
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ishift = iparam(1)
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c levec = iparam(2)
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mxiter = iparam(3)
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c nb = iparam(4)
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nb = 1
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c
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c %--------------------------------------------%
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c | Revision 2 performs only implicit restart. |
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c %--------------------------------------------%
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c
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iupd = 1
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mode = iparam(7)
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c
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if (n .le. 0) then
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ierr = -1
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else if (nev .le. 0) then
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ierr = -2
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else if (ncv .le. nev+1 .or. ncv .gt. n) then
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ierr = -3
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else if (mxiter .le. 0) then
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ierr = 4
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else if (which .ne. 'LM' .and.
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& which .ne. 'SM' .and.
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& which .ne. 'LR' .and.
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& which .ne. 'SR' .and.
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& which .ne. 'LI' .and.
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& which .ne. 'SI') then
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ierr = -5
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else if (bmat .ne. 'I' .and. bmat .ne. 'G') then
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ierr = -6
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else if (lworkl .lt. 3*ncv**2 + 6*ncv) then
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ierr = -7
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else if (mode .lt. 1 .or. mode .gt. 4) then
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ierr = -10
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else if (mode .eq. 1 .and. bmat .eq. 'G') then
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ierr = -11
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else if (ishift .lt. 0 .or. ishift .gt. 1) then
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ierr = -12
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end if
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c
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c %------------%
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c | Error Exit |
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c %------------%
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c
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|
if (ierr .ne. 0) then
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info = ierr
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ido = 99
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go to 9000
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end if
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c
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|
c %------------------------%
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|
c | Set default parameters |
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|
c %------------------------%
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|
c
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|
if (nb .le. 0) nb = 1
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if (tol .le. zero) tol = slamch('EpsMach')
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|
c
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|
c %----------------------------------------------%
|
|
c | NP is the number of additional steps to |
|
|
c | extend the length NEV Lanczos factorization. |
|
|
c | NEV0 is the local variable designating the |
|
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c | size of the invariant subspace desired. |
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c %----------------------------------------------%
|
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c
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np = ncv - nev
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nev0 = nev
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|
c
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|
c %-----------------------------%
|
|
c | Zero out internal workspace |
|
|
c %-----------------------------%
|
|
c
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|
do 10 j = 1, 3*ncv**2 + 6*ncv
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workl(j) = zero
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|
10 continue
|
|
c
|
|
c %-------------------------------------------------------------%
|
|
c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q |
|
|
c | etc... and the remaining workspace. |
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|
c | Also update pointer to be used on output. |
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|
c | Memory is laid out as follows: |
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|
c | workl(1:ncv*ncv) := generated Hessenberg matrix |
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|
c | workl(ncv*ncv+1:ncv*ncv+2*ncv) := real and imaginary |
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|
c | parts of ritz values |
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|
c | workl(ncv*ncv+2*ncv+1:ncv*ncv+3*ncv) := error bounds |
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|
c | workl(ncv*ncv+3*ncv+1:2*ncv*ncv+3*ncv) := rotation matrix Q |
|
|
c | workl(2*ncv*ncv+3*ncv+1:3*ncv*ncv+6*ncv) := workspace |
|
|
c | The final workspace is needed by subroutine sneigh called |
|
|
c | by snaup2. Subroutine sneigh calls LAPACK routines for |
|
|
c | calculating eigenvalues and the last row of the eigenvector |
|
|
c | matrix. |
|
|
c %-------------------------------------------------------------%
|
|
c
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|
ldh = ncv
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|
ldq = ncv
|
|
ih = 1
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|
ritzr = ih + ldh*ncv
|
|
ritzi = ritzr + ncv
|
|
bounds = ritzi + ncv
|
|
iq = bounds + ncv
|
|
iw = iq + ldq*ncv
|
|
next = iw + ncv**2 + 3*ncv
|
|
c
|
|
ipntr(4) = next
|
|
ipntr(5) = ih
|
|
ipntr(6) = ritzr
|
|
ipntr(7) = ritzi
|
|
ipntr(8) = bounds
|
|
ipntr(14) = iw
|
|
c
|
|
end if
|
|
c
|
|
c %-------------------------------------------------------%
|
|
c | Carry out the Implicitly restarted Arnoldi Iteration. |
|
|
c %-------------------------------------------------------%
|
|
c
|
|
call snaup2
|
|
& ( ido, bmat, n, which, nev0, np, tol, resid, mode, iupd,
|
|
& ishift, mxiter, v, ldv, workl(ih), ldh, workl(ritzr),
|
|
& workl(ritzi), workl(bounds), workl(iq), ldq, workl(iw),
|
|
& ipntr, workd, info )
|
|
c
|
|
c %--------------------------------------------------%
|
|
c | ido .ne. 99 implies use of reverse communication |
|
|
c | to compute operations involving OP or shifts. |
|
|
c %--------------------------------------------------%
|
|
c
|
|
if (ido .eq. 3) iparam(8) = np
|
|
if (ido .ne. 99) go to 9000
|
|
c
|
|
iparam(3) = mxiter
|
|
iparam(5) = np
|
|
iparam(9) = nopx
|
|
iparam(10) = nbx
|
|
iparam(11) = nrorth
|
|
c
|
|
c %------------------------------------%
|
|
c | Exit if there was an informational |
|
|
c | error within snaup2. |
|
|
c %------------------------------------%
|
|
c
|
|
if (info .lt. 0) go to 9000
|
|
if (info .eq. 2) info = 3
|
|
c
|
|
if (msglvl .gt. 0) then
|
|
call ivout (logfil, 1, mxiter, ndigit,
|
|
& '_naupd: Number of update iterations taken')
|
|
call ivout (logfil, 1, np, ndigit,
|
|
& '_naupd: Number of wanted "converged" Ritz values')
|
|
call svout (logfil, np, workl(ritzr), ndigit,
|
|
& '_naupd: Real part of the final Ritz values')
|
|
call svout (logfil, np, workl(ritzi), ndigit,
|
|
& '_naupd: Imaginary part of the final Ritz values')
|
|
call svout (logfil, np, workl(bounds), ndigit,
|
|
& '_naupd: Associated Ritz estimates')
|
|
end if
|
|
c
|
|
call second (t1)
|
|
tnaupd = t1 - t0
|
|
c
|
|
if (msglvl .gt. 0) then
|
|
c
|
|
c %--------------------------------------------------------%
|
|
c | Version Number & Version Date are defined in version.h |
|
|
c %--------------------------------------------------------%
|
|
c
|
|
write (6,1000)
|
|
write (6,1100) mxiter, nopx, nbx, nrorth, nitref, nrstrt,
|
|
& tmvopx, tmvbx, tnaupd, tnaup2, tnaitr, titref,
|
|
& tgetv0, tneigh, tngets, tnapps, tnconv, trvec
|
|
1000 format (//,
|
|
& 5x, '=============================================',/
|
|
& 5x, '= Nonsymmetric implicit Arnoldi update code =',/
|
|
& 5x, '= Version Number: ', ' 2.4', 21x, ' =',/
|
|
& 5x, '= Version Date: ', ' 07/31/96', 16x, ' =',/
|
|
& 5x, '=============================================',/
|
|
& 5x, '= Summary of timing statistics =',/
|
|
& 5x, '=============================================',//)
|
|
1100 format (
|
|
& 5x, 'Total number update iterations = ', i5,/
|
|
& 5x, 'Total number of OP*x operations = ', i5,/
|
|
& 5x, 'Total number of B*x operations = ', i5,/
|
|
& 5x, 'Total number of reorthogonalization steps = ', i5,/
|
|
& 5x, 'Total number of iterative refinement steps = ', i5,/
|
|
& 5x, 'Total number of restart steps = ', i5,/
|
|
& 5x, 'Total time in user OP*x operation = ', f12.6,/
|
|
& 5x, 'Total time in user B*x operation = ', f12.6,/
|
|
& 5x, 'Total time in Arnoldi update routine = ', f12.6,/
|
|
& 5x, 'Total time in naup2 routine = ', f12.6,/
|
|
& 5x, 'Total time in basic Arnoldi iteration loop = ', f12.6,/
|
|
& 5x, 'Total time in reorthogonalization phase = ', f12.6,/
|
|
& 5x, 'Total time in (re)start vector generation = ', f12.6,/
|
|
& 5x, 'Total time in Hessenberg eig. subproblem = ', f12.6,/
|
|
& 5x, 'Total time in getting the shifts = ', f12.6,/
|
|
& 5x, 'Total time in applying the shifts = ', f12.6,/
|
|
& 5x, 'Total time in convergence testing = ', f12.6,/
|
|
& 5x, 'Total time in computing final Ritz vectors = ', f12.6/)
|
|
end if
|
|
c
|
|
9000 continue
|
|
c
|
|
return
|
|
c
|
|
c %---------------%
|
|
c | End of snaupd |
|
|
c %---------------%
|
|
c
|
|
end
|