C DSAUPD SOURCE FANDEUR 22/05/02 21:15:15 11359
c-----------------------------------------------------------------------
c\BeginDoc
c
c\Name: dsaupd
c
c\Description:
c
c Reverse communication interface for the Implicitly Restarted Arnoldi
c Iteration. For symmetric problems this reduces to a variant of the Lanczos
c method. This method has been designed to compute approximations to a
c few eigenpairs of a linear operator OP that is real and symmetric
c with respect to a real positive semi-definite symmetric matrix B,
c i.e.
c
c B*OP = (OP`)*B.
c
c Another way to express this condition is
c
c < x,OPy > = < OPx,y > where < z,w > = z`Bw .
c
c In the standard eigenproblem B is the identity matrix.
c ( A` denotes transpose of A)
c
c The computed approximate eigenvalues are called Ritz values and
c the corresponding approximate eigenvectors are called Ritz vectors.
c
c dsaupd is usually called iteratively to solve one of the
c following problems:
c
c Mode 1: A*x = lambda*x, A symmetric
c ===> OP = A and B = I.
c
c Mode 2: A*x = lambda*M*x, A symmetric, M symmetric positive definite
c ===> OP = inv[M]*A and B = M.
c ===> (If M can be factored see remark 3 below)
c
c Mode 3: K*x = lambda*M*x, K symmetric, M symmetric positive semi-definite
c ===> OP = (inv[K - sigma*M])*M and B = M.
c ===> Shift-and-Invert mode
c
c Mode 4: K*x = lambda*KG*x, K symmetric positive semi-definite,
c KG symmetric indefinite
c ===> OP = (inv[K - sigma*KG])*K and B = K.
c ===> Buckling mode
c
c Mode 5: A*x = lambda*M*x, A symmetric, M symmetric positive semi-definite
c ===> OP = inv[A - sigma*M]*[A + sigma*M] and B = M.
c ===> Cayley transformed mode
c
c NOTE: The action of w <- inv[A - sigma*M]*v or w <- inv[M]*v
c should be accomplished either by a direct method
c using a sparse matrix factorization and solving
c
c [A - sigma*M]*w = v or M*w = v,
c
c or through an iterative method for solving these
c systems. If an iterative method is used, the
c convergence test must be more stringent than
c the accuracy requirements for the eigenvalue
c approximations.
c
c\Usage:
c call dsaupd
c ( IDO, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM,
c IPNTR, WORKD, WORKL, LWORKL, INFO )
c
c\Arguments
c IDO Integer. (INPUT/OUTPUT)
c Reverse communication flag. IDO must be zero on the first
c call to dsaupd . IDO will be set internally to
c indicate the type of operation to be performed. Control is
c then given back to the calling routine which has the
c responsibility to carry out the requested operation and call
c dsaupd with the result. The operand is given in
c WORKD(IPNTR(1)), the result must be put in WORKD(IPNTR(2)).
c (If Mode = 2 see remark 5 below)
c -------------------------------------------------------------
c IDO = 0: first call to the reverse communication interface
c IDO = -1: compute Y = OP * X where
c IPNTR(1) is the pointer into WORKD for X,
c IPNTR(2) is the pointer into WORKD for Y.
c This is for the initialization phase to force the
c starting vector into the range of OP.
c IDO = 1: compute Y = OP * X where
c IPNTR(1) is the pointer into WORKD for X,
c IPNTR(2) is the pointer into WORKD for Y.
c In mode 3,4 and 5, the vector B * X is already
c available in WORKD(ipntr(3)). It does not
c need to be recomputed in forming OP * X.
c IDO = 2: compute Y = B * X where
c IPNTR(1) is the pointer into WORKD for X,
c IPNTR(2) is the pointer into WORKD for Y.
c IDO = 3: compute the IPARAM(8) shifts where
c IPNTR(11) is the pointer into WORKL for
c placing the shifts. See remark 6 below.
c IDO = 99: done
c -------------------------------------------------------------
c
c BMAT Character*1. (INPUT)
c BMAT specifies the type of the matrix B that defines the
c semi-inner product for the operator OP.
c B = 'I' -> standard eigenvalue problem A*x = lambda*x
c B = 'G' -> generalized eigenvalue problem A*x = lambda*B*x
c
c N Integer. (INPUT)
c Dimension of the eigenproblem.
c
c WHICH Character*2. (INPUT)
c Specify which of the Ritz values of OP to compute.
c
c 'LA' - compute the NEV largest (algebraic) eigenvalues.
c 'SA' - compute the NEV smallest (algebraic) eigenvalues.
c 'LM' - compute the NEV largest (in magnitude) eigenvalues.
c 'SM' - compute the NEV smallest (in magnitude) eigenvalues.
c 'BE' - compute NEV eigenvalues, half from each end of the
c spectrum. When NEV is odd, compute one more from the
c high end than from the low end.
c (see remark 1 below)
c
c NEV Integer. (INPUT)
c Number of eigenvalues of OP to be computed. 0 < NEV < N.
c
c TOL Double precision scalar. (INPUT)
c Stopping criterion: the relative accuracy of the Ritz value
c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)).
c If TOL .LE. 0. is passed a default is set:
c DEFAULT = DLAMCH ('EPS') (machine precision as computed
c by the LAPACK auxiliary subroutine DLAMCH ).
c
c RESID Double precision array of length N. (INPUT/OUTPUT)
c On INPUT:
c If INFO .EQ. 0, a random initial residual vector is used.
c If INFO .NE. 0, RESID contains the initial residual vector,
c possibly from a previous run.
c On OUTPUT:
c RESID contains the final residual vector.
c
c NCV Integer. (INPUT)
c Number of columns of the matrix V (less than or equal to N).
c This will indicate how many Lanczos vectors are generated
c at each iteration. After the startup phase in which NEV
c Lanczos vectors are generated, the algorithm generates
c NCV-NEV Lanczos vectors at each subsequent update iteration.
c Most of the cost in generating each Lanczos vector is in the
c matrix-vector product OP*x. (See remark 4 below).
c
c V REAL*8 N by NCV array. (OUTPUT)
c The NCV columns of V contain the Lanczos basis vectors.
c
c LDV Integer. (INPUT)
c Leading dimension of V exactly as declared in the calling
c program.
c
c IPARAM Integer array of length 11. (INPUT/OUTPUT)
c IPARAM(1) = ISHIFT: method for selecting the implicit shifts.
c The shifts selected at each iteration are used to restart
c the Arnoldi iteration in an implicit fashion.
c -------------------------------------------------------------
c ISHIFT = 0: the shifts are provided by the user via
c reverse communication. The NCV eigenvalues of
c the current tridiagonal matrix T are returned in
c the part of WORKL array corresponding to RITZ.
c See remark 6 below.
c ISHIFT = 1: exact shifts with respect to the reduced
c tridiagonal matrix T. This is equivalent to
c restarting the iteration with a starting vector
c that is a linear combination of Ritz vectors
c associated with the "wanted" Ritz values.
c -------------------------------------------------------------
c
c IPARAM(2) = LEVEC
c No longer referenced. See remark 2 below.
c
c IPARAM(3) = MXITER
c On INPUT: maximum number of Arnoldi update iterations allowed.
c On OUTPUT: actual number of Arnoldi update iterations taken.
c
c IPARAM(4) = NB: blocksize to be used in the recurrence.
c The code currently works only for NB = 1.
c
c IPARAM(5) = NCONV: number of "converged" Ritz values.
c This represents the number of Ritz values that satisfy
c the convergence criterion.
c
c IPARAM(6) = IUPD
c No longer referenced. Implicit restarting is ALWAYS used.
c
c IPARAM(7) = MODE
c On INPUT determines what type of eigenproblem is being solved.
c Must be 1,2,3,4,5; See under \Description of dsaupd for the
c five modes available.
c
c IPARAM(8) = NP
c When ido = 3 and the user provides shifts through reverse
c communication (IPARAM(1)=0), dsaupd returns NP, the number
c of shifts the user is to provide. 0 < NP <=NCV-NEV. See Remark
c 6 below.
c
c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO,
c OUTPUT: NUMOP = total number of OP*x operations,
c NUMOPB = total number of B*x operations if BMAT='G',
c NUMREO = total number of steps of re-orthogonalization.
c
c IPNTR Integer array of length 11. (OUTPUT)
c Pointer to mark the starting locations in the WORKD and WORKL
c arrays for matrices/vectors used by the Lanczos iteration.
c -------------------------------------------------------------
c IPNTR(1): pointer to the current operand vector X in WORKD.
c IPNTR(2): pointer to the current result vector Y in WORKD.
c IPNTR(3): pointer to the vector B * X in WORKD when used in
c the shift-and-invert mode.
c IPNTR(4): pointer to the next available location in WORKL
c that is untouched by the program.
c IPNTR(5): pointer to the NCV by 2 tridiagonal matrix T in WORKL.
c IPNTR(6): pointer to the NCV RITZ values array in WORKL.
c IPNTR(7): pointer to the Ritz estimates in array WORKL associated
c with the Ritz values located in RITZ in WORKL.
c IPNTR(11): pointer to the NP shifts in WORKL. See Remark 6 below.
c
c Note: IPNTR(8:10) is only referenced by dseupd . See Remark 2.
c IPNTR(8): pointer to the NCV RITZ values of the original system.
c IPNTR(9): pointer to the NCV corresponding error bounds.
c IPNTR(10): pointer to the NCV by NCV matrix of eigenvectors
c of the tridiagonal matrix T. Only referenced by
c dseupd if RVEC = .TRUE. See Remarks.
c -------------------------------------------------------------
c
c WORKD Double precision work array of length 3*N. (REVERSE COMMUNICATION)
c Distributed array to be used in the basic Arnoldi iteration
c for reverse communication. The user should not use WORKD
c as temporary workspace during the iteration. Upon termination
c WORKD(1:N) contains B*RESID(1:N). If the Ritz vectors are desired
c subroutine dseupd uses this output.
c See Data Distribution Note below.
c
c WORKL Double precision work array of length LWORKL. (OUTPUT/WORKSPACE)
c Private (replicated) array on each PE or array allocated on
c the front end. See Data Distribution Note below.
c
c LWORKL Integer. (INPUT)
c LWORKL must be at least NCV**2 + 8*NCV .
c
c INFO Integer. (INPUT/OUTPUT)
c If INFO .EQ. 0, a randomly initial residual vector is used.
c If INFO .NE. 0, RESID contains the initial residual vector,
c possibly from a previous run.
c Error flag on output.
c = 0: Normal exit.
c = 1: Maximum number of iterations taken.
c All possible eigenvalues of OP has been found. IPARAM(5)
c returns the number of wanted converged Ritz values.
c = 2: No longer an informational error. Deprecated starting
c with release 2 of ARPACK.
c = 3: No shifts could be applied during a cycle of the
c Implicitly restarted Arnoldi iteration. One possibility
c is to increase the size of NCV relative to NEV.
c See remark 4 below.
c = -1: N must be positive.
c = -2: NEV must be positive.
c = -3: NCV must be greater than NEV and less than or equal to N.
c = -4: The maximum number of Arnoldi update iterations allowed
c must be greater than zero.
c = -5: WHICH must be one of 'LM', 'SM', 'LA', 'SA' or 'BE'.
c = -6: BMAT must be one of 'I' or 'G'.
c = -7: Length of private work array WORKL is not sufficient.
c = -8: Error return from trid. eigenvalue calculation;
c Informatinal error from LAPACK routine dsteqr .
c = -9: Starting vector is zero.
c = -10: IPARAM(7) must be 1,2,3,4,5.
c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatable.
c = -12: IPARAM(1) must be equal to 0 or 1.
c = -13: NEV and WHICH = 'BE' are incompatable.
c = -9999: Could not build an Arnoldi factorization.
c IPARAM(5) returns the size of the current Arnoldi
c factorization. The user is advised to check that
c enough workspace and array storage has been allocated.
c
c
c\Remarks
c 1. The converged Ritz values are always returned in ascending
c algebraic order. The computed Ritz values are approximate
c eigenvalues of OP. The selection of WHICH should be made
c with this in mind when Mode = 3,4,5. After convergence,
c approximate eigenvalues of the original problem may be obtained
c with the ARPACK subroutine dseupd .
c
c 2. If the Ritz vectors corresponding to the converged Ritz values
c are needed, the user must call dseupd immediately following completion
c of dsaupd . This is new starting with version 2.1 of ARPACK.
c
c 3. If M can be factored into a Cholesky factorization M = LL`
c then Mode = 2 should not be selected. Instead one should use
c Mode = 1 with OP = inv(L)*A*inv(L`). Appropriate triangular
c linear systems should be solved with L and L` rather
c than computing inverses. After convergence, an approximate
c eigenvector z of the original problem is recovered by solving
c L`z = x where x is a Ritz vector of OP.
c
c 4. At present there is no a-priori analysis to guide the selection
c of NCV relative to NEV. The only formal requrement is that NCV > NEV.
c However, it is recommended that NCV .ge. 2*NEV. If many problems of
c the same type are to be solved, one should experiment with increasing
c NCV while keeping NEV fixed for a given test problem. This will
c usually decrease the required number of OP*x operations but it
c also increases the work and storage required to maintain the orthogonal
c basis vectors. The optimal "cross-over" with respect to CPU time
c is problem dependent and must be determined empirically.
c
c 5. If IPARAM(7) = 2 then in the Reverse commuication interface the user
c must do the following. When IDO = 1, Y = OP * X is to be computed.
c When IPARAM(7) = 2 OP = inv(B)*A. After computing A*X the user
c must overwrite X with A*X. Y is then the solution to the linear set
c of equations B*Y = A*X.
c
c 6. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the
c NP = IPARAM(8) shifts in locations:
c 1 WORKL(IPNTR(11))
c 2 WORKL(IPNTR(11)+1)
c .
c .
c .
c NP WORKL(IPNTR(11)+NP-1).
c
c The eigenvalues of the current tridiagonal matrix are located in
c WORKL(IPNTR(6)) through WORKL(IPNTR(6)+NCV-1). They are in the
c order defined by WHICH. The associated Ritz estimates are located in
c WORKL(IPNTR(8)), WORKL(IPNTR(8)+1), ... , WORKL(IPNTR(8)+NCV-1).
c
c-----------------------------------------------------------------------
c
c\Data Distribution Note:
c
c Fortran-D syntax:
c ================
c REAL RESID(N), V(LDV,NCV), WORKD(3*N), WORKL(LWORKL)
c DECOMPOSE D1(N), D2(N,NCV)
c ALIGN RESID(I) with D1(I)
c ALIGN V(I,J) with D2(I,J)
c ALIGN WORKD(I) with D1(I) range (1:N)
c ALIGN WORKD(I) with D1(I-N) range (N+1:2*N)
c ALIGN WORKD(I) with D1(I-2*N) range (2*N+1:3*N)
c DISTRIBUTE D1(BLOCK), D2(BLOCK,:)
c REPLICATED WORKL(LWORKL)
c
c Cray MPP syntax:
c ===============
c REAL RESID(N), V(LDV,NCV), WORKD(N,3), WORKL(LWORKL)
c SHARED RESID(BLOCK), V(BLOCK,:), WORKD(BLOCK,:)
c REPLICATED WORKL(LWORKL)
c
c
c\BeginLib
c
c\References:
c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in
c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992),
c pp 357-385.
c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
c Restarted Arnoldi Iteration", Rice University Technical Report
c TR95-13, Department of Computational and Applied Mathematics.
c 3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall,
c 1980.
c 4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos Program",
c Computer Physics Communications, 53 (1989), pp 169-179.
c 5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to
c Implement the Spectral Transformation", Math. Comp., 48 (1987),
c pp 663-673.
c 6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos
c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems",
c SIAM J. Matr. Anal. Apps., January (1993).
c 7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines
c for Updating the QR decomposition", ACM TOMS, December 1990,
c Volume 16 Number 4, pp 369-377.
c 8. R.B. Lehoucq, D.C. Sorensen, "Implementation of Some Spectral
c Transformations in a k-Step Arnoldi Method". In Preparation.
c
c\Routines called:
c dsaup2 ARPACK routine that implements the Implicitly Restarted
c Arnoldi Iteration.
c dstats ARPACK routine that initialize timing and other statistics
c variables.
c ivout ARPACK utility routine that prints integers.
c arscnd ARPACK utility routine for timing. -> deleted by BP in 2020
c dvout ARPACK utility routine that prints vectors.
c dlamch LAPACK routine that determines machine constants.
c
c\Authors
c Danny Sorensen Phuong Vu
c Richard Lehoucq CRPC / Rice University
c Dept. of Computational & Houston, Texas
c Applied Mathematics
c Rice University
c Houston, Texas
c
c\Revision history:
c 12/15/93: Version ' 2.4'
c
c\SCCS Information: @(#)
c FILE: saupd.F SID: 2.8 DATE OF SID: 04/10/01 RELEASE: 2
c
c\Remarks
c 1. None
c
c\EndLib
c
c-----------------------------------------------------------------------
c
subroutine dsaupd
& ( ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam,
& ipntr, workd, workl, lworkl, ITRAK, info )
c
c %----------------------------------------------------%
c | Include files for debugging and timing information |
c -INC TARTRAK
c %----------------------------------------------------%
c
c
c %------------------%
c | Scalar Arguments |
c %------------------%
c
character bmat*1, which*2
integer ido, info, ldv, lworkl, n, ncv, nev
REAL*8
& tol
c real*8 T0,T1
c
c %-----------------%
c | Array Arguments |
c %-----------------%
c
integer iparam(11), ipntr(11)
INTEGER ITRAK(5)
REAL*8
& resid(n), v(ldv,ncv), workd(3*n), workl(lworkl)
c
c %------------%
c | Parameters |
c %------------%
c
REAL*8
& one, zero
parameter (one = 1.0D+0 , zero = 0.0D+0 )
c
c %---------------%
c | Local Scalars |
c %---------------%
c
integer bounds, ierr, ih, iq, ishift, iupd, iw,
& ldh, ldq, msglvl, mxiter, mode, nb,
& nev0, next, np, ritz, j
save bounds, ierr, ih, iq, ishift, iupd, iw,
c & ldh, ldq, msglvl, mxiter, mode, nb,
& ldh, ldq, mxiter, mode, nb,
& nev0, next, np, ritz
parameter (msglvl=0)
c
c %----------------------%
c | External Subroutines |
c %----------------------%
c
external dsaup2 , dvout , ivout, dstats
c
c %--------------------%
c | External Functions |
c %--------------------%
c
REAL*8
& dlamch
external dlamch
c
c %-----------------------%
c | Executable Statements |
c %-----------------------%
c T0=0.D0
c T1=0.D0
nopx =ITRAK(1)
nbx =ITRAK(2)
nrorth=ITRAK(3)
nitref=ITRAK(4)
nrstrt=ITRAK(5)
c
if (ido .eq. 0) then
c
c %-------------------------------%
c | Initialize timing statistics |
c | & message level for debugging |
c %-------------------------------%
c
call dstats(nopx,nbx,nrorth,nitref,nrstrt)
* call arscnd (t0)
c msglvl = msaupd
c
ierr = 0
ishift = iparam(1)
mxiter = iparam(3)
c nb = iparam(4)
nb = 1
c
c %--------------------------------------------%
c | Revision 2 performs only implicit restart. |
c %--------------------------------------------%
c
iupd = 1
mode = iparam(7)
c
c %----------------%
c | Error checking |
c %----------------%
c
if (n .le. 0) then
ierr = -1
else if (nev .le. 0) then
ierr = -2
else if (ncv .le. nev .or. ncv .gt. n) then
ierr = -3
end if
c
c %----------------------------------------------%
c | NP is the number of additional steps to |
c | extend the length NEV Lanczos factorization. |
c %----------------------------------------------%
c
np = ncv - nev
c
if (mxiter .le. 0) ierr = -4
if (which .ne. 'LM' .and.
& which .ne. 'SM' .and.
& which .ne. 'LA' .and.
& which .ne. 'SA' .and.
& which .ne. 'BE') ierr = -5
if (bmat .ne. 'I' .and. bmat .ne. 'G') ierr = -6
c
if (lworkl .lt. ncv**2 + 8*ncv) ierr = -7
if (mode .lt. 1 .or. mode .gt. 5) then
ierr = -10
else if (mode .eq. 1 .and. bmat .eq. 'G') then
ierr = -11
else if (ishift .lt. 0 .or. ishift .gt. 1) then
ierr = -12
else if (nev .eq. 1 .and. which .eq. 'BE') then
ierr = -13
end if
c
c %------------%
c | Error Exit |
c %------------%
c
if (ierr .ne. 0) then
info = ierr
ido = 99
go to 9000
end if
c
c %------------------------%
c | Set default parameters |
c %------------------------%
c
if (nb .le. 0) nb = 1
if (tol .le. zero) tol = dlamch ('EpsMach')
c
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 |
c | size of the invariant subspace desired. |
c %----------------------------------------------%
c
np = ncv - nev
nev0 = nev
c
c %-----------------------------%
c | Zero out internal workspace |
c %-----------------------------%
c
do 10 j = 1, ncv**2 + 8*ncv
workl(j) = zero
10 continue
c
c %-------------------------------------------------------%
c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q |
c | etc... and the remaining workspace. |
c | Also update pointer to be used on output. |
c | Memory is laid out as follows: |
c | workl(1:2*ncv) := generated tridiagonal matrix |
c | workl(2*ncv+1:2*ncv+ncv) := ritz values |
c | workl(3*ncv+1:3*ncv+ncv) := computed error bounds |
c | workl(4*ncv+1:4*ncv+ncv*ncv) := rotation matrix Q |
c | workl(4*ncv+ncv*ncv+1:7*ncv+ncv*ncv) := workspace |
c %-------------------------------------------------------%
c
ldh = ncv
ldq = ncv
ih = 1
ritz = ih + 2*ldh
bounds = ritz + ncv
iq = bounds + ncv
iw = iq + ncv**2
next = iw + 3*ncv
c
ipntr(4) = next
ipntr(5) = ih
ipntr(6) = ritz
ipntr(7) = bounds
ipntr(11) = iw
end if
c
c %-------------------------------------------------------%
c | Carry out the Implicitly restarted Lanczos Iteration. |
c %-------------------------------------------------------%
c
call dsaup2
& ( ido, bmat, n, which, nev0, np, tol, resid, mode, iupd,
& ishift, mxiter, v, ldv, workl(ih), ldh, workl(ritz),
& workl(bounds), workl(iq), ldq, workl(iw), ipntr, workd,
& ITRAK, info )
c recup
nopx =ITRAK(1)
nbx =ITRAK(2)
nrorth=ITRAK(3)
nitref=ITRAK(4)
nrstrt=ITRAK(5)
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 dsaup2 . |
c %------------------------------------%
c
if (info .lt. 0) go to 9000
if (info .eq. 2) info = 3
c
if (msglvl .gt. 0) then
call ivout ( 1, mxiter, ndigit,
& '_saupd: number of update iterations taken')
call ivout ( 1, np, ndigit,
& '_saupd: number of "converged" Ritz values')
call dvout ( np, workl(Ritz), ndigit,
& '_saupd: final Ritz values')
call dvout ( np, workl(Bounds), ndigit,
& '_saupd: corresponding error bounds')
end if
c
* call arscnd (t1)
c tsaupd = 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
c & ,tmvopx, tmvbx, tsaupd, tsaup2, tsaitr, titref,
c & tgetv0, tseigt, tsgets, tsapps, tsconv
1000 format (//,
& 5x, '==========================================',/
& 5x, '= Symmetric implicit Arnoldi update code =',/
& 5x, '= Version Number:', ' 2.4' , 19x, ' =',/
& 5x, '= Version Date: ', ' 07/31/96' , 14x, ' =',/
& 5x, '==========================================',//)
c & 5x, '= Summary of timing statistics =',/
c & 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,/)
c & 5x, 'Total time in user OP*x operation = ', f12.6,/
c & 5x, 'Total time in user B*x operation = ', f12.6,/
c & 5x, 'Total time in Arnoldi update routine = ', f12.6,/
c & 5x, 'Total time in saup2 routine = ', f12.6,/
c & 5x, 'Total time in basic Arnoldi iteration loop = ', f12.6,/
c & 5x, 'Total time in reorthogonalization phase = ', f12.6,/
c & 5x, 'Total time in (re)start vector generation = ', f12.6,/
c & 5x, 'Total time in trid eigenvalue subproblem = ', f12.6,/
c & 5x, 'Total time in getting the shifts = ', f12.6,/
c & 5x, 'Total time in applying the shifts = ', f12.6,/
c & 5x, 'Total time in convergence testing = ', f12.6)
end if
c
9000 continue
c
c ITRAK(..)=... inutile car ITRAK fourni a dsaup2 par ex et pas modifie ici
c
c
c %---------------%
c | End of dsaupd |
c %---------------%
c
end