org.netlib.arpack
Class Ssaup2

java.lang.Object
  extended by org.netlib.arpack.Ssaup2

public class Ssaup2
extends java.lang.Object

Following is the description from the original
Fortran source.  For each array argument, the Java
version will include an integer offset parameter, so
the arguments may not match the description exactly.
Contact seymour@cs.utk.edu with any questions.

*----------------------------------------------------------------------- \BeginDoc \Name: ssaup2 \Description: Intermediate level interface called by ssaupd. \Usage: call ssaup2 ( IDO, BMAT, N, WHICH, NEV, NP, TOL, RESID, MODE, IUPD, ISHIFT, MXITER, V, LDV, H, LDH, RITZ, BOUNDS, Q, LDQ, WORKL, IPNTR, WORKD, INFO ) \Arguments IDO, BMAT, N, WHICH, NEV, TOL, RESID: same as defined in ssaupd. MODE, ISHIFT, MXITER: see the definition of IPARAM in ssaupd. NP Integer. (INPUT/OUTPUT) Contains the number of implicit shifts to apply during each Arnoldi/Lanczos iteration. If ISHIFT=1, NP is adjusted dynamically at each iteration to accelerate convergence and prevent stagnation. This is also roughly equal to the number of matrix-vector products (involving the operator OP) per Arnoldi iteration. The logic for adjusting is contained within the current subroutine. If ISHIFT=0, NP is the number of shifts the user needs to provide via reverse comunication. 0 < NP < NCV-NEV. NP may be less than NCV-NEV since a leading block of the current upper Tridiagonal matrix has split off and contains "unwanted" Ritz values. Upon termination of the IRA iteration, NP contains the number of "converged" wanted Ritz values. IUPD Integer. (INPUT) IUPD .EQ. 0: use explicit restart instead implicit update. IUPD .NE. 0: use implicit update. V Real N by (NEV+NP) array. (INPUT/OUTPUT) The Lanczos basis vectors. LDV Integer. (INPUT) Leading dimension of V exactly as declared in the calling program. H Real (NEV+NP) by 2 array. (OUTPUT) H is used to store the generated symmetric tridiagonal matrix The subdiagonal is stored in the first column of H starting at H(2,1). The main diagonal is stored in the second column of H starting at H(1,2). If ssaup2 converges store the B-norm of the final residual vector in H(1,1). LDH Integer. (INPUT) Leading dimension of H exactly as declared in the calling program. RITZ Real array of length NEV+NP. (OUTPUT) RITZ(1:NEV) contains the computed Ritz values of OP. BOUNDS Real array of length NEV+NP. (OUTPUT) BOUNDS(1:NEV) contain the error bounds corresponding to RITZ. Q Real (NEV+NP) by (NEV+NP) array. (WORKSPACE) Private (replicated) work array used to accumulate the rotation in the shift application step. LDQ Integer. (INPUT) Leading dimension of Q exactly as declared in the calling program. WORKL Real array of length at least 3*(NEV+NP). (INPUT/WORKSPACE) Private (replicated) array on each PE or array allocated on the front end. It is used in the computation of the tridiagonal eigenvalue problem, the calculation and application of the shifts and convergence checking. If ISHIFT .EQ. O and IDO .EQ. 3, the first NP locations of WORKL are used in reverse communication to hold the user supplied shifts. IPNTR Integer array of length 3. (OUTPUT) Pointer to mark the starting locations in the WORKD for vectors used by the Lanczos iteration. ------------------------------------------------------------- IPNTR(1): pointer to the current operand vector X. IPNTR(2): pointer to the current result vector Y. IPNTR(3): pointer to the vector B * X when used in one of the spectral transformation modes. X is the current operand. ------------------------------------------------------------- WORKD Real work array of length 3*N. (REVERSE COMMUNICATION) Distributed array to be used in the basic Lanczos iteration for reverse communication. The user should not use WORKD as temporary workspace during the iteration !!!!!!!!!! See Data Distribution Note in ssaupd. INFO Integer. (INPUT/OUTPUT) If INFO .EQ. 0, a randomly initial residual vector is used. If INFO .NE. 0, RESID contains the initial residual vector, possibly from a previous run. Error flag on output. = 0: Normal return. = 1: All possible eigenvalues of OP has been found. NP returns the size of the invariant subspace spanning the operator OP. = 2: No shifts could be applied. = -8: Error return from trid. eigenvalue calculation; This should never happen. = -9: Starting vector is zero. = -9999: Could not build an Lanczos factorization. Size that was built in returned in NP. \EndDoc ----------------------------------------------------------------------- \BeginLib \References: 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), pp 357-385. 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly Restarted Arnoldi Iteration", Rice University Technical Report TR95-13, Department of Computational and Applied Mathematics. 3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall, 1980. 4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos Program", Computer Physics Communications, 53 (1989), pp 169-179. 5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to Implement the Spectral Transformation", Math. Comp., 48 (1987), pp 663-673. 6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", SIAM J. Matr. Anal. Apps., January (1993). 7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines for Updating the QR decomposition", ACM TOMS, December 1990, Volume 16 Number 4, pp 369-377. \Routines called: sgetv0 ARPACK initial vector generation routine. ssaitr ARPACK Lanczos factorization routine. ssapps ARPACK application of implicit shifts routine. ssconv ARPACK convergence of Ritz values routine. sseigt ARPACK compute Ritz values and error bounds routine. ssgets ARPACK reorder Ritz values and error bounds routine. ssortr ARPACK sorting routine. ivout ARPACK utility routine that prints integers. second ARPACK utility routine for timing. svout ARPACK utility routine that prints vectors. slamch LAPACK routine that determines machine constants. scopy Level 1 BLAS that copies one vector to another. sdot Level 1 BLAS that computes the scalar product of two vectors. snrm2 Level 1 BLAS that computes the norm of a vector. sscal Level 1 BLAS that scales a vector. sswap Level 1 BLAS that swaps two vectors. \Author Danny Sorensen Phuong Vu Richard Lehoucq CRPC / Rice University Dept. of Computational & Houston, Texas Applied Mathematics Rice University Houston, Texas \Revision history: 12/15/93: Version ' 2.4' xx/xx/95: Version ' 2.4'. (R.B. Lehoucq) \SCCS Information: @(#) FILE: saup2.F SID: 2.7 DATE OF SID: 5/19/98 RELEASE: 2 \EndLib -----------------------------------------------------------------------


Field Summary
static boolean cnorm
           
static float eps23
           
static boolean getv0
           
static boolean initv
           
static org.netlib.util.intW iter
           
static int kplusp
           
static int msglvl
           
static org.netlib.util.intW nconv
           
static int nev0
           
static int np0
           
static org.netlib.util.floatW rnorm
           
static org.netlib.util.floatW t0
           
static org.netlib.util.floatW t1
           
static org.netlib.util.floatW t2
           
static org.netlib.util.floatW t3
           
static float t4
           
static float t5
           
static boolean update
           
static boolean ushift
           
 
Constructor Summary
Ssaup2()
           
 
Method Summary
static void ssaup2(org.netlib.util.intW ido, java.lang.String bmat, int n, java.lang.String which, org.netlib.util.intW nev, org.netlib.util.intW np, float tol, float[] resid, int _resid_offset, int mode, int iupd, int ishift, org.netlib.util.intW mxiter, float[] v, int _v_offset, int ldv, float[] h, int _h_offset, int ldh, float[] ritz, int _ritz_offset, float[] bounds, int _bounds_offset, float[] q, int _q_offset, int ldq, float[] workl, int _workl_offset, int[] ipntr, int _ipntr_offset, float[] workd, int _workd_offset, org.netlib.util.intW info)
           
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

t0

public static org.netlib.util.floatW t0

t1

public static org.netlib.util.floatW t1

t2

public static org.netlib.util.floatW t2

t3

public static org.netlib.util.floatW t3

t4

public static float t4

t5

public static float t5

cnorm

public static boolean cnorm

getv0

public static boolean getv0

initv

public static boolean initv

update

public static boolean update

ushift

public static boolean ushift

iter

public static org.netlib.util.intW iter

kplusp

public static int kplusp

msglvl

public static int msglvl

nconv

public static org.netlib.util.intW nconv

nev0

public static int nev0

np0

public static int np0

rnorm

public static org.netlib.util.floatW rnorm

eps23

public static float eps23
Constructor Detail

Ssaup2

public Ssaup2()
Method Detail

ssaup2

public static void ssaup2(org.netlib.util.intW ido,
                          java.lang.String bmat,
                          int n,
                          java.lang.String which,
                          org.netlib.util.intW nev,
                          org.netlib.util.intW np,
                          float tol,
                          float[] resid,
                          int _resid_offset,
                          int mode,
                          int iupd,
                          int ishift,
                          org.netlib.util.intW mxiter,
                          float[] v,
                          int _v_offset,
                          int ldv,
                          float[] h,
                          int _h_offset,
                          int ldh,
                          float[] ritz,
                          int _ritz_offset,
                          float[] bounds,
                          int _bounds_offset,
                          float[] q,
                          int _q_offset,
                          int ldq,
                          float[] workl,
                          int _workl_offset,
                          int[] ipntr,
                          int _ipntr_offset,
                          float[] workd,
                          int _workd_offset,
                          org.netlib.util.intW info)