All Packages  Class Hierarchy  This Package  Previous  Next  Index

Class org.netlib.lapack.Dgehd2

java.lang.Object
   |
   +----org.netlib.lapack.Dgehd2

public class Dgehd2

extends 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.

 *     ..
 *
 *  Purpose
 *  =======
 *
 *  DGEHD2 reduces a real general matrix A to upper Hessenberg form H by
 *  an orthogonal similarity transformation:  Q' * A * Q = H .
 *
 *  Arguments
 *  =========
 *
 *  N       (input) INTEGER
 *          The order of the matrix A.  N >= 0.
 *
 *  ILO     (input) INTEGER
 *  IHI     (input) INTEGER
 *          It is assumed that A is already upper triangular in rows
 *          and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
 *          set by a previous call to DGEBAL; otherwise they should be
 *          set to 1 and N respectively. See Further Details.
 *          1 <= ILO <= IHI <= max(1,N).
 *
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 *          On entry, the n by n general matrix to be reduced.
 *          On exit, the upper triangle and the first subdiagonal of A
 *          are overwritten with the upper Hessenberg matrix H, and the
 *          elements below the first subdiagonal, with the array TAU,
 *          represent the orthogonal matrix Q as a product of elementary
 *          reflectors. See Further Details.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
 *
 *  TAU     (output) DOUBLE PRECISION array, dimension (N-1)
 *          The scalar factors of the elementary reflectors (see Further
 *          Details).
 *
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (N)
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit.
 *          < 0:  if INFO = -i, the i-th argument had an illegal value.
 *
 *  Further Details
 *  ===============
 *
 *  The matrix Q is represented as a product of (ihi-ilo) elementary
 *  reflectors
 *
 *     Q = H(ilo) H(ilo+1) . . . H(ihi-1).
 *
 *  Each H(i) has the form
 *
 *     H(i) = I - tau * v * v'
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
 *  exit in A(i+2:ihi,i), and tau in TAU(i).
 *
 *  The contents of A are illustrated by the following example, with
 *  n = 7, ilo = 2 and ihi = 6:
 *
 *  on entry,                        on exit,
 *
 *  ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a )
 *  (     a   a   a   a   a   a )    (      a   h   h   h   h   a )
 *  (     a   a   a   a   a   a )    (      h   h   h   h   h   h )
 *  (     a   a   a   a   a   a )    (      v2  h   h   h   h   h )
 *  (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h )
 *  (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h )
 *  (                         a )    (                          a )
 *
 *  where a denotes an element of the original matrix A, h denotes a
 *  modified element of the upper Hessenberg matrix H, and vi denotes an
 *  element of the vector defining H(i).
 *
 *  =====================================================================
 *
 *     .. Parameters ..

Dgehd2()

dgehd2(int, int, int, double[], int, int, double[], int, double[], int, intW)

 public Dgehd2()

 public static void dgehd2(int n,
                           int ilo,
                           int ihi,
                           double a[],
                           int _a_offset,
                           int lda,
                           double tau[],
                           int _tau_offset,
                           double work[],
                           int _work_offset,
                           intW info)

All Packages  Class Hierarchy  This Package  Previous  Next  Index