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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Fri, 28 Jan 2011 14:04:33 -0500 |
| parents | |
| children | 126d8fe48a12 |
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c\BeginDoc c c\Name: dseupd c c\Description: c c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) the corresponding approximate eigenvectors, c c (2) an orthonormal (Lanczos) basis for the associated approximate c invariant subspace, c c (3) Both. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c (Lanczos) basis is always computed. There is an additional storage cost c of n*nev if both are requested (in this case a separate array Z must be c supplied). c c These quantities are obtained from the Lanczos factorization computed c by DSAUPD for the linear operator OP prescribed by the MODE selection c (see IPARAM(7) in DSAUPD documentation.) DSAUPD must be called before c this routine is called. These approximate eigenvalues and vectors are c commonly called Ritz values and Ritz vectors respectively. They are c referred to as such in the comments that follow. The computed orthonormal c basis for the invariant subspace corresponding to these Ritz values is c referred to as a Lanczos basis. c c See documentation in the header of the subroutine DSAUPD for a definition c of OP as well as other terms and the relation of computed Ritz values c and vectors of OP with respect to the given problem A*z = lambda*B*z. c c The approximate eigenvalues of the original problem are returned in c ascending algebraic order. The user may elect to call this routine c once for each desired Ritz vector and store it peripherally if desired. c There is also the option of computing a selected set of these vectors c with a single call. c c\Usage: c call dseupd c ( RVEC, HOWMNY, SELECT, D, Z, LDZ, SIGMA, BMAT, N, WHICH, NEV, TOL, c RESID, NCV, V, LDV, IPARAM, IPNTR, WORKD, WORKL, LWORKL, INFO ) c c RVEC LOGICAL (INPUT) c Specifies whether Ritz vectors corresponding to the Ritz value c approximations to the eigenproblem A*z = lambda*B*z are computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute Ritz vectors. c c HOWMNY Character*1 (INPUT) c Specifies how many Ritz vectors are wanted and the form of Z c the matrix of Ritz vectors. See remark 1 below. c = 'A': compute NEV Ritz vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT/WORKSPACE) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the Ritz vector corresponding to a c Ritz value D(j), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' , SELECT is used as a workspace for c reordering the Ritz values. c c D Double precision array of dimension NEV. (OUTPUT) c On exit, D contains the Ritz value approximations to the c eigenvalues of A*z = lambda*B*z. The values are returned c in ascending order. If IPARAM(7) = 3,4,5 then D represents c the Ritz values of OP computed by dsaupd transformed to c those of the original eigensystem A*z = lambda*B*z. If c IPARAM(7) = 1,2 then the Ritz values of OP are the same c as the those of A*z = lambda*B*z. c c Z Double precision N by NEV array if HOWMNY = 'A'. (OUTPUT) c On exit, Z contains the B-orthonormal Ritz vectors of the c eigensystem A*z = lambda*B*z corresponding to the Ritz c value approximations. c If RVEC = .FALSE. then Z is not referenced. c NOTE: The array Z may be set equal to first NEV columns of the c Arnoldi/Lanczos basis array V computed by DSAUPD . c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ .ge. max( 1, N ). In any case, LDZ .ge. 1. c c SIGMA Double precision (INPUT) c If IPARAM(7) = 3,4,5 represents the shift. Not referenced if c IPARAM(7) = 1 or 2. c c c **** The remaining arguments MUST be the same as for the **** c **** call to DSAUPD that was just completed. **** c c NOTE: The remaining arguments c c BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, IPNTR, c WORKD, WORKL, LWORKL, INFO c c must be passed directly to DSEUPD following the last call c to DSAUPD . These arguments MUST NOT BE MODIFIED between c the the last call to DSAUPD and the call to DSEUPD . c c Two of these parameters (WORKL, INFO) are also output parameters: c c WORKL Double precision work array of length LWORKL. (OUTPUT/WORKSPACE) c WORKL(1:4*ncv) contains information obtained in c dsaupd . They are not changed by dseupd . c WORKL(4*ncv+1:ncv*ncv+8*ncv) holds the c untransformed Ritz values, the computed error estimates, c and the associated eigenvector matrix of H. c c Note: IPNTR(8:10) contains the pointer into WORKL for addresses c of the above information computed by dseupd . c ------------------------------------------------------------- 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 INFO Integer. (OUTPUT) c Error flag on output. c = 0: Normal exit. 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 = -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 WORKL array is not sufficient. c = -8: Error return from trid. eigenvalue calculation; c Information 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 incompatible. c = -12: NEV and WHICH = 'BE' are incompatible. c = -14: DSAUPD did not find any eigenvalues to sufficient c accuracy. c = -15: HOWMNY must be one of 'A' or 'S' if RVEC = .true. c = -16: HOWMNY = 'S' not yet implemented c = -17: DSEUPD got a different count of the number of converged c Ritz values than DSAUPD got. This indicates the user c probably made an error in passing data from DSAUPD to c DSEUPD or that the data was modified before entering c DSEUPD . 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 c\Remarks c 1. The converged Ritz values are always returned in increasing c (algebraic) order. c c 2. Currently only HOWMNY = 'A' is implemented. It is included at this c stage for the user who wants to incorporate it. c c\Routines called: c dsesrt ARPACK routine that sorts an array X, and applies the c corresponding permutation to a matrix A. c dsortr dsortr ARPACK sorting routine. c ivout ARPACK utility routine that prints integers. c dvout ARPACK utility routine that prints vectors. c dgeqr2 LAPACK routine that computes the QR factorization of c a matrix. c dlacpy LAPACK matrix copy routine. c dlamch LAPACK routine that determines machine constants. c dorm2r LAPACK routine that applies an orthogonal matrix in c factored form. c dsteqr LAPACK routine that computes eigenvalues and eigenvectors c of a tridiagonal matrix. c dger Level 2 BLAS rank one update to a matrix. c dcopy Level 1 BLAS that copies one vector to another . c dnrm2 Level 1 BLAS that computes the norm of a vector. c dscal Level 1 BLAS that scales a vector. c dswap Level 1 BLAS that swaps the contents of two vectors. c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Chao Yang Houston, Texas c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/15/93: Version ' 2.1' c c\SCCS Information: @(#) c FILE: seupd.F SID: 2.11 DATE OF SID: 04/10/01 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- subroutine dseupd (rvec , howmny, select, d , & z , ldz , sigma , bmat , & n , which , nev , tol , & resid , ncv , v , ldv , & iparam, ipntr , workd , workl, & lworkl, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat, howmny, which*2 logical rvec integer info, ldz, ldv, lworkl, n, ncv, nev Double precision & sigma, tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(7), ipntr(11) logical select(ncv) Double precision & d(nev) , resid(n) , v(ldv,ncv), & z(ldz, nev), workd(2*n), workl(lworkl) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0 , zero = 0.0D+0 ) c c %---------------% c | Local Scalars | c %---------------% c character type*6 integer bounds , ierr , ih , ihb , ihd , & iq , iw , j , k , ldh , & ldq , mode , msglvl, nconv , next , & ritz , irz , ibd , np , ishift, & leftptr, rghtptr, numcnv, jj Double precision & bnorm2 , rnorm, temp, temp1, eps23 logical reord c c %----------------------% c | External Subroutines | c %----------------------% c external dcopy , dger , dgeqr2 , dlacpy , dorm2r , dscal , & dsesrt , dsteqr , dswap , dvout , ivout , dsortr c c %--------------------% c | External Functions | c %--------------------% c Double precision & dnrm2 , dlamch external dnrm2 , dlamch c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic min c c %-----------------------% c | Executable Statements | c %-----------------------% c c %------------------------% c | Set default parameters | c %------------------------% c msglvl = mseupd mode = iparam(7) nconv = iparam(5) info = 0 c c %--------------% c | Quick return | c %--------------% c if (nconv .eq. 0) go to 9000 ierr = 0 c if (nconv .le. 0) ierr = -14 if (n .le. 0) ierr = -1 if (nev .le. 0) ierr = -2 if (ncv .le. nev .or. ncv .gt. n) ierr = -3 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 if ( (howmny .ne. 'A' .and. & howmny .ne. 'P' .and. & howmny .ne. 'S') .and. rvec ) & ierr = -15 if (rvec .and. howmny .eq. 'S') ierr = -16 c if (rvec .and. lworkl .lt. ncv**2+8*ncv) ierr = -7 c if (mode .eq. 1 .or. mode .eq. 2) then type = 'REGULR' else if (mode .eq. 3 ) then type = 'SHIFTI' else if (mode .eq. 4 ) then type = 'BUCKLE' else if (mode .eq. 5 ) then type = 'CAYLEY' else ierr = -10 end if if (mode .eq. 1 .and. bmat .eq. 'G') ierr = -11 if (nev .eq. 1 .and. which .eq. 'BE') ierr = -12 c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr go to 9000 end if 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 H | c | The subdiagonal is stored in workl(2:ncv). | c | The dead spot is workl(1) but upon exiting | c | dsaupd stores the B-norm of the last residual | c | vector in workl(1). We use this !!! | c | workl(2*ncv+1:2*ncv+ncv) := ritz values | c | The wanted values are in the first NCONV spots. | c | workl(3*ncv+1:3*ncv+ncv) := computed Ritz estimates | c | The wanted values are in the first NCONV spots. | c | NOTE: workl(1:4*ncv) is set by dsaupd and is not | c | modified by dseupd . | c %-------------------------------------------------------% c c %-------------------------------------------------------% c | The following is used and set by dseupd . | c | workl(4*ncv+1:4*ncv+ncv) := used as workspace during | c | computation of the eigenvectors of H. Stores | c | the diagonal of H. Upon EXIT contains the NCV | c | Ritz values of the original system. The first | c | NCONV spots have the wanted values. If MODE = | c | 1 or 2 then will equal workl(2*ncv+1:3*ncv). | c | workl(5*ncv+1:5*ncv+ncv) := used as workspace during | c | computation of the eigenvectors of H. Stores | c | the subdiagonal of H. Upon EXIT contains the | c | NCV corresponding Ritz estimates of the | c | original system. The first NCONV spots have the | c | wanted values. If MODE = 1,2 then will equal | c | workl(3*ncv+1:4*ncv). | c | workl(6*ncv+1:6*ncv+ncv*ncv) := orthogonal Q that is | c | the eigenvector matrix for H as returned by | c | dsteqr . Not referenced if RVEC = .False. | c | Ordering follows that of workl(4*ncv+1:5*ncv) | c | workl(6*ncv+ncv*ncv+1:6*ncv+ncv*ncv+2*ncv) := | c | Workspace. Needed by dsteqr and by dseupd . | c | GRAND total of NCV*(NCV+8) locations. | c %-------------------------------------------------------% c c ih = ipntr(5) ritz = ipntr(6) bounds = ipntr(7) ldh = ncv ldq = ncv ihd = bounds + ldh ihb = ihd + ldh iq = ihb + ldh iw = iq + ldh*ncv next = iw + 2*ncv ipntr(4) = next ipntr(8) = ihd ipntr(9) = ihb ipntr(10) = iq c c %----------------------------------------% c | irz points to the Ritz values computed | c | by _seigt before exiting _saup2. | c | ibd points to the Ritz estimates | c | computed by _seigt before exiting | c | _saup2. | c %----------------------------------------% c irz = ipntr(11)+ncv ibd = irz+ncv c c c %---------------------------------% c | Set machine dependent constant. | c %---------------------------------% c eps23 = dlamch ('Epsilon-Machine') eps23 = eps23**(2.0D+0 / 3.0D+0 ) c c %---------------------------------------% c | RNORM is B-norm of the RESID(1:N). | c | BNORM2 is the 2 norm of B*RESID(1:N). | c | Upon exit of dsaupd WORKD(1:N) has | c | B*RESID(1:N). | c %---------------------------------------% c rnorm = workl(ih) if (bmat .eq. 'I') then bnorm2 = rnorm else if (bmat .eq. 'G') then bnorm2 = dnrm2 (n, workd, 1) end if c if (msglvl .gt. 2) then call dvout (logfil, ncv, workl(irz), ndigit, & '_seupd: Ritz values passed in from _SAUPD.') call dvout (logfil, ncv, workl(ibd), ndigit, & '_seupd: Ritz estimates passed in from _SAUPD.') end if c if (rvec) then c reord = .false. c c %---------------------------------------------------% c | Use the temporary bounds array to store indices | c | These will be used to mark the select array later | c %---------------------------------------------------% c do 10 j = 1,ncv workl(bounds+j-1) = j select(j) = .false. 10 continue c c %-------------------------------------% c | Select the wanted Ritz values. | c | Sort the Ritz values so that the | c | wanted ones appear at the tailing | c | NEV positions of workl(irr) and | c | workl(iri). Move the corresponding | c | error estimates in workl(bound) | c | accordingly. | c %-------------------------------------% c np = ncv - nev ishift = 0 call dsgets (ishift, which , nev , & np , workl(irz) , workl(bounds), & workl) c if (msglvl .gt. 2) then call dvout (logfil, ncv, workl(irz), ndigit, & '_seupd: Ritz values after calling _SGETS.') call dvout (logfil, ncv, workl(bounds), ndigit, & '_seupd: Ritz value indices after calling _SGETS.') end if c c %-----------------------------------------------------% c | Record indices of the converged wanted Ritz values | c | Mark the select array for possible reordering | c %-----------------------------------------------------% c numcnv = 0 do 11 j = 1,ncv temp1 = max(eps23, abs(workl(irz+ncv-j)) ) jj = workl(bounds + ncv - j) if (numcnv .lt. nconv .and. & workl(ibd+jj-1) .le. tol*temp1) then select(jj) = .true. numcnv = numcnv + 1 if (jj .gt. nev) reord = .true. endif 11 continue c c %-----------------------------------------------------------% c | Check the count (numcnv) of converged Ritz values with | c | the number (nconv) reported by _saupd. If these two | c | are different then there has probably been an error | c | caused by incorrect passing of the _saupd data. | c %-----------------------------------------------------------% c if (msglvl .gt. 2) then call ivout(logfil, 1, numcnv, ndigit, & '_seupd: Number of specified eigenvalues') call ivout(logfil, 1, nconv, ndigit, & '_seupd: Number of "converged" eigenvalues') end if c if (numcnv .ne. nconv) then info = -17 go to 9000 end if c c %-----------------------------------------------------------% c | Call LAPACK routine _steqr to compute the eigenvalues and | c | eigenvectors of the final symmetric tridiagonal matrix H. | c | Initialize the eigenvector matrix Q to the identity. | c %-----------------------------------------------------------% c call dcopy (ncv-1, workl(ih+1), 1, workl(ihb), 1) call dcopy (ncv, workl(ih+ldh), 1, workl(ihd), 1) c call dsteqr ('Identity', ncv, workl(ihd), workl(ihb), & workl(iq) , ldq, workl(iw), ierr) c if (ierr .ne. 0) then info = -8 go to 9000 end if c if (msglvl .gt. 1) then call dcopy (ncv, workl(iq+ncv-1), ldq, workl(iw), 1) call dvout (logfil, ncv, workl(ihd), ndigit, & '_seupd: NCV Ritz values of the final H matrix') call dvout (logfil, ncv, workl(iw), ndigit, & '_seupd: last row of the eigenvector matrix for H') end if c if (reord) then c c %---------------------------------------------% c | Reordered the eigenvalues and eigenvectors | c | computed by _steqr so that the "converged" | c | eigenvalues appear in the first NCONV | c | positions of workl(ihd), and the associated | c | eigenvectors appear in the first NCONV | c | columns. | c %---------------------------------------------% c leftptr = 1 rghtptr = ncv c if (ncv .eq. 1) go to 30 c 20 if (select(leftptr)) then c c %-------------------------------------------% c | Search, from the left, for the first Ritz | c | value that has not converged. | c %-------------------------------------------% c leftptr = leftptr + 1 c else if ( .not. select(rghtptr)) then c c %----------------------------------------------% c | Search, from the right, the first Ritz value | c | that has converged. | c %----------------------------------------------% c rghtptr = rghtptr - 1 c else c c %----------------------------------------------% c | Swap the Ritz value on the left that has not | c | converged with the Ritz value on the right | c | that has converged. Swap the associated | c | eigenvector of the tridiagonal matrix H as | c | well. | c %----------------------------------------------% c temp = workl(ihd+leftptr-1) workl(ihd+leftptr-1) = workl(ihd+rghtptr-1) workl(ihd+rghtptr-1) = temp call dcopy (ncv, workl(iq+ncv*(leftptr-1)), 1, & workl(iw), 1) call dcopy (ncv, workl(iq+ncv*(rghtptr-1)), 1, & workl(iq+ncv*(leftptr-1)), 1) call dcopy (ncv, workl(iw), 1, & workl(iq+ncv*(rghtptr-1)), 1) leftptr = leftptr + 1 rghtptr = rghtptr - 1 c end if c if (leftptr .lt. rghtptr) go to 20 c 30 end if c if (msglvl .gt. 2) then call dvout (logfil, ncv, workl(ihd), ndigit, & '_seupd: The eigenvalues of H--reordered') end if c c %----------------------------------------% c | Load the converged Ritz values into D. | c %----------------------------------------% c call dcopy (nconv, workl(ihd), 1, d, 1) c else c c %-----------------------------------------------------% c | Ritz vectors not required. Load Ritz values into D. | c %-----------------------------------------------------% c call dcopy (nconv, workl(ritz), 1, d, 1) call dcopy (ncv, workl(ritz), 1, workl(ihd), 1) c end if c c %------------------------------------------------------------------% c | Transform the Ritz values and possibly vectors and corresponding | c | Ritz estimates of OP to those of A*x=lambda*B*x. The Ritz values | c | (and corresponding data) are returned in ascending order. | c %------------------------------------------------------------------% c if (type .eq. 'REGULR') then c c %---------------------------------------------------------% c | Ascending sort of wanted Ritz values, vectors and error | c | bounds. Not necessary if only Ritz values are desired. | c %---------------------------------------------------------% c if (rvec) then call dsesrt ('LA', rvec , nconv, d, ncv, workl(iq), ldq) else call dcopy (ncv, workl(bounds), 1, workl(ihb), 1) end if c else c c %-------------------------------------------------------------% c | * Make a copy of all the Ritz values. | c | * Transform the Ritz values back to the original system. | c | For TYPE = 'SHIFTI' the transformation is | c | lambda = 1/theta + sigma | c | For TYPE = 'BUCKLE' the transformation is | c | lambda = sigma * theta / ( theta - 1 ) | c | For TYPE = 'CAYLEY' the transformation is | c | lambda = sigma * (theta + 1) / (theta - 1 ) | c | where the theta are the Ritz values returned by dsaupd . | c | NOTES: | c | *The Ritz vectors are not affected by the transformation. | c | They are only reordered. | c %-------------------------------------------------------------% c call dcopy (ncv, workl(ihd), 1, workl(iw), 1) if (type .eq. 'SHIFTI') then do 40 k=1, ncv workl(ihd+k-1) = one / workl(ihd+k-1) + sigma 40 continue else if (type .eq. 'BUCKLE') then do 50 k=1, ncv workl(ihd+k-1) = sigma * workl(ihd+k-1) / & (workl(ihd+k-1) - one) 50 continue else if (type .eq. 'CAYLEY') then do 60 k=1, ncv workl(ihd+k-1) = sigma * (workl(ihd+k-1) + one) / & (workl(ihd+k-1) - one) 60 continue end if c c %-------------------------------------------------------------% c | * Store the wanted NCONV lambda values into D. | c | * Sort the NCONV wanted lambda in WORKL(IHD:IHD+NCONV-1) | c | into ascending order and apply sort to the NCONV theta | c | values in the transformed system. We will need this to | c | compute Ritz estimates in the original system. | c | * Finally sort the lambda`s into ascending order and apply | c | to Ritz vectors if wanted. Else just sort lambda`s into | c | ascending order. | c | NOTES: | c | *workl(iw:iw+ncv-1) contain the theta ordered so that they | c | match the ordering of the lambda. We`ll use them again for | c | Ritz vector purification. | c %-------------------------------------------------------------% c call dcopy (nconv, workl(ihd), 1, d, 1) call dsortr ('LA', .true., nconv, workl(ihd), workl(iw)) if (rvec) then call dsesrt ('LA', rvec , nconv, d, ncv, workl(iq), ldq) else call dcopy (ncv, workl(bounds), 1, workl(ihb), 1) call dscal (ncv, bnorm2/rnorm, workl(ihb), 1) call dsortr ('LA', .true., nconv, d, workl(ihb)) end if c end if c c %------------------------------------------------% c | Compute the Ritz vectors. Transform the wanted | c | eigenvectors of the symmetric tridiagonal H by | c | the Lanczos basis matrix V. | c %------------------------------------------------% c if (rvec .and. howmny .eq. 'A') then c c %----------------------------------------------------------% c | Compute the QR factorization of the matrix representing | c | the wanted invariant subspace located in the first NCONV | c | columns of workl(iq,ldq). | c %----------------------------------------------------------% c call dgeqr2 (ncv, nconv , workl(iq) , & ldq, workl(iw+ncv), workl(ihb), & ierr) c c %--------------------------------------------------------% c | * Postmultiply V by Q. | c | * Copy the first NCONV columns of VQ into Z. | c | The N by NCONV matrix Z is now a matrix representation | c | of the approximate invariant subspace associated with | c | the Ritz values in workl(ihd). | c %--------------------------------------------------------% c call dorm2r ('Right', 'Notranspose', n , & ncv , nconv , workl(iq), & ldq , workl(iw+ncv), v , & ldv , workd(n+1) , ierr) call dlacpy ('All', n, nconv, v, ldv, z, ldz) c c %-----------------------------------------------------% c | In order to compute the Ritz estimates for the Ritz | c | values in both systems, need the last row of the | c | eigenvector matrix. Remember, it`s in factored form | c %-----------------------------------------------------% c do 65 j = 1, ncv-1 workl(ihb+j-1) = zero 65 continue workl(ihb+ncv-1) = one call dorm2r ('Left', 'Transpose' , ncv , & 1 , nconv , workl(iq) , & ldq , workl(iw+ncv), workl(ihb), & ncv , temp , ierr) c else if (rvec .and. howmny .eq. 'S') then c c Not yet implemented. See remark 2 above. c end if c if (type .eq. 'REGULR' .and. rvec) then c do 70 j=1, ncv workl(ihb+j-1) = rnorm * abs( workl(ihb+j-1) ) 70 continue c else if (type .ne. 'REGULR' .and. rvec) then c c %-------------------------------------------------% c | * Determine Ritz estimates of the theta. | c | If RVEC = .true. then compute Ritz estimates | c | of the theta. | c | If RVEC = .false. then copy Ritz estimates | c | as computed by dsaupd . | c | * Determine Ritz estimates of the lambda. | c %-------------------------------------------------% c call dscal (ncv, bnorm2, workl(ihb), 1) if (type .eq. 'SHIFTI') then c do 80 k=1, ncv workl(ihb+k-1) = abs( workl(ihb+k-1) ) & / workl(iw+k-1)**2 80 continue c else if (type .eq. 'BUCKLE') then c do 90 k=1, ncv workl(ihb+k-1) = sigma * abs( workl(ihb+k-1) ) & / (workl(iw+k-1)-one )**2 90 continue c else if (type .eq. 'CAYLEY') then c do 100 k=1, ncv workl(ihb+k-1) = abs( workl(ihb+k-1) & / workl(iw+k-1)*(workl(iw+k-1)-one) ) 100 continue c end if c end if c if (type .ne. 'REGULR' .and. msglvl .gt. 1) then call dvout (logfil, nconv, d, ndigit, & '_seupd: Untransformed converged Ritz values') call dvout (logfil, nconv, workl(ihb), ndigit, & '_seupd: Ritz estimates of the untransformed Ritz values') else if (msglvl .gt. 1) then call dvout (logfil, nconv, d, ndigit, & '_seupd: Converged Ritz values') call dvout (logfil, nconv, workl(ihb), ndigit, & '_seupd: Associated Ritz estimates') end if c c %-------------------------------------------------% c | Ritz vector purification step. Formally perform | c | one of inverse subspace iteration. Only used | c | for MODE = 3,4,5. See reference 7 | c %-------------------------------------------------% c if (rvec .and. (type .eq. 'SHIFTI' .or. type .eq. 'CAYLEY')) then c do 110 k=0, nconv-1 workl(iw+k) = workl(iq+k*ldq+ncv-1) & / workl(iw+k) 110 continue c else if (rvec .and. type .eq. 'BUCKLE') then c do 120 k=0, nconv-1 workl(iw+k) = workl(iq+k*ldq+ncv-1) & / (workl(iw+k)-one) 120 continue c end if c if (type .ne. 'REGULR') & call dger (n, nconv, one, resid, 1, workl(iw), 1, z, ldz) c 9000 continue c return c c %---------------% c | End of dseupd | c %---------------% c end