691 lines
28 KiB
Fortran
691 lines
28 KiB
Fortran
c-----------------------------------------------------------------------
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c\BeginDoc
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c
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c\Name: ssaupd
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c
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c\Description:
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c
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c Reverse communication interface for the Implicitly Restarted Arnoldi
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c Iteration. For symmetric problems this reduces to a variant of the Lanczos
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c method. This method has been designed to compute approximations to a
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c few eigenpairs of a linear operator OP that is real and symmetric
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c with respect to a real positive semi-definite symmetric matrix B,
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c i.e.
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c
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c B*OP = (OP`)*B.
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c
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c Another way to express this condition is
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c
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c < x,OPy > = < OPx,y > where < z,w > = z`Bw .
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c
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c In the standard eigenproblem B is the identity matrix.
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c ( A` denotes transpose of A)
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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 ssaupd 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, A symmetric
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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, A symmetric, 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: K*x = lambda*M*x, K symmetric, M symmetric positive semi-definite
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c ===> OP = (inv[K - sigma*M])*M and B = M.
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c ===> Shift-and-Invert mode
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c
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c Mode 4: K*x = lambda*KG*x, K symmetric positive semi-definite,
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c KG symmetric indefinite
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c ===> OP = (inv[K - sigma*KG])*K and B = K.
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c ===> Buckling mode
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c
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c Mode 5: A*x = lambda*M*x, A symmetric, M symmetric positive semi-definite
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c ===> OP = inv[A - sigma*M]*[A + sigma*M] and B = M.
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c ===> Cayley transformed mode
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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 ssaupd
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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 ssaupd. 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 ssaupd 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 (If Mode = 2 see remark 5 below)
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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 3,4 and 5, 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) shifts where
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c IPNTR(11) is the pointer into WORKL for
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c placing the shifts. See remark 6 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 B = 'I' -> standard eigenvalue problem A*x = lambda*x
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c B = '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 Specify which of the Ritz values of OP to compute.
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c
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c 'LA' - compute the NEV largest (algebraic) eigenvalues.
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c 'SA' - compute the NEV smallest (algebraic) eigenvalues.
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c 'LM' - compute the NEV largest (in magnitude) eigenvalues.
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c 'SM' - compute the NEV smallest (in magnitude) eigenvalues.
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c 'BE' - compute NEV eigenvalues, half from each end of the
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c spectrum. When NEV is odd, compute one more from the
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c high end than from the low end.
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c (see remark 1 below)
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c
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c NEV Integer. (INPUT)
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c Number of eigenvalues of OP to be computed. 0 < NEV < N.
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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 If TOL .LE. 0. is passed a default is set:
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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 (less than or equal to N).
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c This will indicate how many Lanczos vectors are generated
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c at each iteration. After the startup phase in which NEV
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c Lanczos vectors are generated, the algorithm generates
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c NCV-NEV Lanczos vectors at each subsequent update iteration.
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c Most of the cost in generating each Lanczos vector is in the
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c matrix-vector product OP*x. (See remark 4 below).
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c
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c V Real N by NCV array. (OUTPUT)
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c The NCV columns of V contain the Lanczos 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
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c 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 NCV eigenvalues of
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c the current tridiagonal matrix T are returned in
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c the part of WORKL array corresponding to RITZ.
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c See remark 6 below.
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c ISHIFT = 1: exact shifts with respect to the reduced
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c tridiagonal matrix T. 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 Ritz vectors
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c associated with the "wanted" Ritz values.
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c -------------------------------------------------------------
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c
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c IPARAM(2) = LEVEC
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c No longer referenced. See remark 2 below.
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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 1,2,3,4,5; See under \Description of ssaupd for the
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c five 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), ssaupd 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 6 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 11. (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 Lanczos 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 2 tridiagonal matrix T in WORKL.
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c IPNTR(6): pointer to the NCV RITZ values array in WORKL.
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c IPNTR(7): pointer to the Ritz estimates in array WORKL associated
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c with the Ritz values located in RITZ in WORKL.
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c IPNTR(11): pointer to the NP shifts in WORKL. See Remark 6 below.
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c
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c Note: IPNTR(8:10) is only referenced by sseupd. See Remark 2.
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c IPNTR(8): pointer to the NCV RITZ values of the original system.
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c IPNTR(9): pointer to the NCV corresponding error bounds.
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c IPNTR(10): pointer to the NCV by NCV matrix of eigenvectors
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c of the tridiagonal matrix T. Only referenced by
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c sseupd if RVEC = .TRUE. See Remarks.
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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 the Ritz vectors are desired
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c subroutine sseupd 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 NCV**2 + 8*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 must be greater than NEV and less than or equal to N.
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c = -4: The maximum number of Arnoldi update iterations allowed
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c must be greater than zero.
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c = -5: WHICH must be one of 'LM', 'SM', 'LA', 'SA' or 'BE'.
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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 WORKL is not sufficient.
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c = -8: Error return from trid. eigenvalue calculation;
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c Informatinal error from LAPACK routine ssteqr.
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c = -9: Starting vector is zero.
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c = -10: IPARAM(7) must be 1,2,3,4,5.
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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 = -13: NEV and WHICH = 'BE' are incompatable.
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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. The user is advised to check that
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c enough workspace and array storage has been allocated.
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c
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c
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c\Remarks
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c 1. The converged Ritz values are always returned in ascending
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c algebraic order. The computed Ritz values are approximate
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c eigenvalues of OP. The selection of WHICH should be made
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c with this in mind when Mode = 3,4,5. After convergence,
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c approximate eigenvalues of the original problem may be obtained
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c with the ARPACK subroutine sseupd.
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c
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c 2. If the Ritz vectors corresponding to the converged Ritz values
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c are needed, the user must call sseupd immediately following completion
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c of ssaupd. This is new starting with version 2.1 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.
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c However, it is recommended that NCV .ge. 2*NEV. 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
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c 5. If IPARAM(7) = 2 then in the Reverse commuication interface the user
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c must do the following. When IDO = 1, Y = OP * X is to be computed.
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c When IPARAM(7) = 2 OP = inv(B)*A. After computing A*X the user
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c must overwrite X with A*X. Y is then the solution to the linear set
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c of equations B*Y = A*X.
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c
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c 6. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the
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c NP = IPARAM(8) shifts in locations:
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c 1 WORKL(IPNTR(11))
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c 2 WORKL(IPNTR(11)+1)
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c .
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c .
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c .
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c NP WORKL(IPNTR(11)+NP-1).
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c
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c The eigenvalues of the current tridiagonal matrix are located in
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c WORKL(IPNTR(6)) through WORKL(IPNTR(6)+NCV-1). They are in the
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c order defined by WHICH. 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
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c\BeginLib
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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, "The Symmetric Eigenvalue Problem". Prentice-Hall,
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c 1980.
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c 4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos Program",
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c Computer Physics Communications, 53 (1989), pp 169-179.
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c 5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to
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c Implement the Spectral Transformation", Math. Comp., 48 (1987),
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c pp 663-673.
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c 6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos
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c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems",
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c SIAM J. Matr. Anal. Apps., January (1993).
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c 7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines
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c for Updating the QR decomposition", ACM TOMS, December 1990,
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c Volume 16 Number 4, pp 369-377.
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c 8. R.B. Lehoucq, D.C. Sorensen, "Implementation of Some Spectral
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c Transformations in a k-Step Arnoldi Method". In Preparation.
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c
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c\Routines called:
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c ssaup2 ARPACK routine that implements the Implicitly Restarted
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c Arnoldi Iteration.
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c sstats ARPACK routine that initialize timing and other statistics
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c variables.
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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\Authors
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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 12/15/93: Version ' 2.4'
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c
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c\SCCS Information: @(#)
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c FILE: saupd.F SID: 2.8 DATE OF SID: 04/10/01 RELEASE: 2
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c
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c\Remarks
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c 1. None
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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 ssaupd
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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(11)
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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, msglvl, mxiter, mode, nb,
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& nev0, next, np, ritz, j
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save bounds, ierr, ih, iq, ishift, iupd, iw,
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& ldh, ldq, msglvl, mxiter, mode, nb,
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& nev0, next, np, ritz
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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 ssaup2, svout, ivout, second, sstats
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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 sstats
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call second (t0)
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msglvl = msaupd
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c
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ierr = 0
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ishift = iparam(1)
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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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c %----------------%
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c | Error checking |
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c %----------------%
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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 .or. ncv .gt. n) then
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ierr = -3
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end if
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c
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c %----------------------------------------------%
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c | NP is the number of additional steps to |
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c | extend the length NEV Lanczos factorization. |
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c %----------------------------------------------%
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c
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np = ncv - nev
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c
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if (mxiter .le. 0) ierr = -4
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if (which .ne. 'LM' .and.
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& which .ne. 'SM' .and.
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& which .ne. 'LA' .and.
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& which .ne. 'SA' .and.
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& which .ne. 'BE') ierr = -5
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if (bmat .ne. 'I' .and. bmat .ne. 'G') ierr = -6
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c
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if (lworkl .lt. ncv**2 + 8*ncv) ierr = -7
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if (mode .lt. 1 .or. mode .gt. 5) 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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else if (nev .eq. 1 .and. which .eq. 'BE') then
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ierr = -13
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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 %----------------------------------------------%
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c | NP is the number of additional steps to |
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c | extend the length NEV Lanczos factorization. |
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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 %-----------------------------%
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c | Zero out internal workspace |
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c %-----------------------------%
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c
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do 10 j = 1, ncv**2 + 8*ncv
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workl(j) = zero
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10 continue
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c
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c %-------------------------------------------------------%
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c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q |
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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(1:2*ncv) := generated tridiagonal matrix |
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c | workl(2*ncv+1:2*ncv+ncv) := ritz values |
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c | workl(3*ncv+1:3*ncv+ncv) := computed error bounds |
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c | workl(4*ncv+1:4*ncv+ncv*ncv) := rotation matrix Q |
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c | workl(4*ncv+ncv*ncv+1:7*ncv+ncv*ncv) := workspace |
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c %-------------------------------------------------------%
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c
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ldh = ncv
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ldq = ncv
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ih = 1
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ritz = ih + 2*ldh
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bounds = ritz + ncv
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iq = bounds + ncv
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iw = iq + ncv**2
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next = iw + 3*ncv
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c
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ipntr(4) = next
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ipntr(5) = ih
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ipntr(6) = ritz
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ipntr(7) = bounds
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ipntr(11) = iw
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end if
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c
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c %-------------------------------------------------------%
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c | Carry out the Implicitly restarted Lanczos Iteration. |
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c %-------------------------------------------------------%
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c
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call ssaup2
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& ( ido, bmat, n, which, nev0, np, tol, resid, mode, iupd,
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& ishift, mxiter, v, ldv, workl(ih), ldh, workl(ritz),
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& workl(bounds), workl(iq), ldq, workl(iw), ipntr, workd,
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& info )
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c
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c %--------------------------------------------------%
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c | ido .ne. 99 implies use of reverse communication |
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c | to compute operations involving OP or shifts. |
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c %--------------------------------------------------%
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c
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if (ido .eq. 3) iparam(8) = np
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if (ido .ne. 99) go to 9000
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c
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iparam(3) = mxiter
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iparam(5) = np
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iparam(9) = nopx
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iparam(10) = nbx
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iparam(11) = nrorth
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c
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c %------------------------------------%
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c | Exit if there was an informational |
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c | error within ssaup2. |
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c %------------------------------------%
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c
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if (info .lt. 0) go to 9000
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if (info .eq. 2) info = 3
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c
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if (msglvl .gt. 0) then
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call ivout (logfil, 1, mxiter, ndigit,
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& '_saupd: number of update iterations taken')
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call ivout (logfil, 1, np, ndigit,
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& '_saupd: number of "converged" Ritz values')
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call svout (logfil, np, workl(Ritz), ndigit,
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& '_saupd: final Ritz values')
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call svout (logfil, np, workl(Bounds), ndigit,
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& '_saupd: corresponding error bounds')
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end if
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c
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call second (t1)
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tsaupd = t1 - t0
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c
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if (msglvl .gt. 0) then
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c
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c %--------------------------------------------------------%
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c | Version Number & Version Date are defined in version.h |
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c %--------------------------------------------------------%
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c
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write (6,1000)
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write (6,1100) mxiter, nopx, nbx, nrorth, nitref, nrstrt,
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& tmvopx, tmvbx, tsaupd, tsaup2, tsaitr, titref,
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& tgetv0, tseigt, tsgets, tsapps, tsconv
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1000 format (//,
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& 5x, '==========================================',/
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& 5x, '= Symmetric implicit Arnoldi update code =',/
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& 5x, '= Version Number:', ' 2.4' , 19x, ' =',/
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& 5x, '= Version Date: ', ' 07/31/96' , 14x, ' =',/
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& 5x, '==========================================',/
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& 5x, '= Summary of timing statistics =',/
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& 5x, '==========================================',//)
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1100 format (
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& 5x, 'Total number update iterations = ', i5,/
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& 5x, 'Total number of OP*x operations = ', i5,/
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& 5x, 'Total number of B*x operations = ', i5,/
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& 5x, 'Total number of reorthogonalization steps = ', i5,/
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& 5x, 'Total number of iterative refinement steps = ', i5,/
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& 5x, 'Total number of restart steps = ', i5,/
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& 5x, 'Total time in user OP*x operation = ', f12.6,/
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& 5x, 'Total time in user B*x operation = ', f12.6,/
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& 5x, 'Total time in Arnoldi update routine = ', f12.6,/
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& 5x, 'Total time in saup2 routine = ', f12.6,/
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& 5x, 'Total time in basic Arnoldi iteration loop = ', f12.6,/
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& 5x, 'Total time in reorthogonalization phase = ', f12.6,/
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& 5x, 'Total time in (re)start vector generation = ', f12.6,/
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& 5x, 'Total time in trid eigenvalue subproblem = ', f12.6,/
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& 5x, 'Total time in getting the shifts = ', f12.6,/
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& 5x, 'Total time in applying the shifts = ', f12.6,/
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& 5x, 'Total time in convergence testing = ', f12.6)
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end if
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c
|
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9000 continue
|
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c
|
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return
|
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c
|
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c %---------------%
|
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c | End of ssaupd |
|
|
c %---------------%
|
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c
|
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end
|