org.netlib.arpack
Class Dnapps

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

public class Dnapps
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: dnapps \Description: Given the Arnoldi factorization A*V_{k} - V_{k}*H_{k} = r_{k+p}*e_{k+p}^T, apply NP implicit shifts resulting in A*(V_{k}*Q) - (V_{k}*Q)*(Q^T* H_{k}*Q) = r_{k+p}*e_{k+p}^T * Q where Q is an orthogonal matrix which is the product of rotations and reflections resulting from the NP bulge chage sweeps. The updated Arnoldi factorization becomes: A*VNEW_{k} - VNEW_{k}*HNEW_{k} = rnew_{k}*e_{k}^T. \Usage: call dnapps ( N, KEV, NP, SHIFTR, SHIFTI, V, LDV, H, LDH, RESID, Q, LDQ, WORKL, WORKD ) \Arguments N Integer. (INPUT) Problem size, i.e. size of matrix A. KEV Integer. (INPUT/OUTPUT) KEV+NP is the size of the input matrix H. KEV is the size of the updated matrix HNEW. KEV is only updated on ouput when fewer than NP shifts are applied in order to keep the conjugate pair together. NP Integer. (INPUT) Number of implicit shifts to be applied. SHIFTR, Double precision array of length NP. (INPUT) SHIFTI Real and imaginary part of the shifts to be applied. Upon, entry to dnapps, the shifts must be sorted so that the conjugate pairs are in consecutive locations. V Double precision N by (KEV+NP) array. (INPUT/OUTPUT) On INPUT, V contains the current KEV+NP Arnoldi vectors. On OUTPUT, V contains the updated KEV Arnoldi vectors in the first KEV columns of V. LDV Integer. (INPUT) Leading dimension of V exactly as declared in the calling program. H Double precision (KEV+NP) by (KEV+NP) array. (INPUT/OUTPUT) On INPUT, H contains the current KEV+NP by KEV+NP upper Hessenber matrix of the Arnoldi factorization. On OUTPUT, H contains the updated KEV by KEV upper Hessenberg matrix in the KEV leading submatrix. LDH Integer. (INPUT) Leading dimension of H exactly as declared in the calling program. RESID Double precision array of length N. (INPUT/OUTPUT) On INPUT, RESID contains the the residual vector r_{k+p}. On OUTPUT, RESID is the update residual vector rnew_{k} in the first KEV locations. Q Double precision KEV+NP by KEV+NP work array. (WORKSPACE) Work array used to accumulate the rotations and reflections during the bulge chase sweep. LDQ Integer. (INPUT) Leading dimension of Q exactly as declared in the calling program. WORKL Double precision work array of length (KEV+NP). (WORKSPACE) Private (replicated) array on each PE or array allocated on the front end. WORKD Double precision work array of length 2*N. (WORKSPACE) Distributed array used in the application of the accumulated orthogonal matrix Q. \EndDoc ----------------------------------------------------------------------- \BeginLib \Local variables: xxxxxx real \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. \Routines called: ivout ARPACK utility routine that prints integers. second ARPACK utility routine for timing. dmout ARPACK utility routine that prints matrices. dvout ARPACK utility routine that prints vectors. dlabad LAPACK routine that computes machine constants. dlacpy LAPACK matrix copy routine. dlamch LAPACK routine that determines machine constants. dlanhs LAPACK routine that computes various norms of a matrix. dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. dlarf LAPACK routine that applies Householder reflection to a matrix. dlarfg LAPACK Householder reflection construction routine. dlartg LAPACK Givens rotation construction routine. dlaset LAPACK matrix initialization routine. dgemv Level 2 BLAS routine for matrix vector multiplication. daxpy Level 1 BLAS that computes a vector triad. dcopy Level 1 BLAS that copies one vector to another . dscal Level 1 BLAS that scales a vector. \Author Danny Sorensen Phuong Vu Richard Lehoucq CRPC / Rice University Dept. of Computational & Houston, Texas Applied Mathematics Rice University Houston, Texas \Revision history: xx/xx/92: Version ' 2.4' \SCCS Information: @(#) FILE: napps.F SID: 2.4 DATE OF SID: 3/28/97 RELEASE: 2 \Remarks 1. In this version, each shift is applied to all the sublocks of the Hessenberg matrix H and not just to the submatrix that it comes from. Deflation as in LAPACK routine dlahqr (QR algorithm for upper Hessenberg matrices ) is used. The subdiagonals of H are enforced to be non-negative. \EndLib -----------------------------------------------------------------------


Field Summary
static boolean first
           
static org.netlib.util.doubleW ovfl
           
static double smlnum
           
static org.netlib.util.floatW t0
           
static org.netlib.util.floatW t1
           
static float t2
           
static float t3
           
static float t4
           
static float t5
           
static double ulp
           
static org.netlib.util.doubleW unfl
           
 
Constructor Summary
Dnapps()
           
 
Method Summary
static void dnapps(int n, org.netlib.util.intW kev, int np, double[] shiftr, int _shiftr_offset, double[] shifti, int _shifti_offset, double[] v, int _v_offset, int ldv, double[] h, int _h_offset, int ldh, double[] resid, int _resid_offset, double[] q, int _q_offset, int ldq, double[] workl, int _workl_offset, double[] workd, int _workd_offset)
           
 
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 float t2

t3

public static float t3

t4

public static float t4

t5

public static float t5

ovfl

public static org.netlib.util.doubleW ovfl

smlnum

public static double smlnum

ulp

public static double ulp

unfl

public static org.netlib.util.doubleW unfl

first

public static boolean first
Constructor Detail

Dnapps

public Dnapps()
Method Detail

dnapps

public static void dnapps(int n,
                          org.netlib.util.intW kev,
                          int np,
                          double[] shiftr,
                          int _shiftr_offset,
                          double[] shifti,
                          int _shifti_offset,
                          double[] v,
                          int _v_offset,
                          int ldv,
                          double[] h,
                          int _h_offset,
                          int ldh,
                          double[] resid,
                          int _resid_offset,
                          double[] q,
                          int _q_offset,
                          int ldq,
                          double[] workl,
                          int _workl_offset,
                          double[] workd,
                          int _workd_offset)