org.netlib.lapack
Class DLAHRD
java.lang.Object
org.netlib.lapack.DLAHRD
public class DLAHRD
 extends java.lang.Object
DLAHRD is a simplified interface to the JLAPACK routine dlahrd.
This interface converts Javastyle 2D rowmajor arrays into
the 1D columnmajor linearized arrays expected by the lower
level JLAPACK routines. Using this interface also allows you
to omit offset and leading dimension arguments. However, because
of these conversions, these routines will be slower than the low
level ones. Following is the description from the original Fortran
source. Contact seymour@cs.utk.edu with any questions.
* ..
*
* Purpose
* =======
*
* DLAHRD reduces the first NB columns of a real general nby(nk+1)
* matrix A so that elements below the kth subdiagonal are zero. The
* reduction is performed by an orthogonal similarity transformation
* Q' * A * Q. The routine returns the matrices V and T which determine
* Q as a block reflector I  V*T*V', and also the matrix Y = A * V * T.
*
* This is an auxiliary routine called by DGEHRD.
*
* Arguments
* =========
*
* N (input) INTEGER
* The order of the matrix A.
*
* K (input) INTEGER
* The offset for the reduction. Elements below the kth
* subdiagonal in the first NB columns are reduced to zero.
*
* NB (input) INTEGER
* The number of columns to be reduced.
*
* A (input/output) DOUBLE PRECISION array, dimension (LDA,NK+1)
* On entry, the nby(nk+1) general matrix A.
* On exit, the elements on and above the kth subdiagonal in
* the first NB columns are overwritten with the corresponding
* elements of the reduced matrix; the elements below the kth
* subdiagonal, with the array TAU, represent the matrix Q as a
* product of elementary reflectors. The other columns of A are
* unchanged. See Further Details.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* TAU (output) DOUBLE PRECISION array, dimension (NB)
* The scalar factors of the elementary reflectors. See Further
* Details.
*
* T (output) DOUBLE PRECISION array, dimension (LDT,NB)
* The upper triangular matrix T.
*
* LDT (input) INTEGER
* The leading dimension of the array T. LDT >= NB.
*
* Y (output) DOUBLE PRECISION array, dimension (LDY,NB)
* The nbynb matrix Y.
*
* LDY (input) INTEGER
* The leading dimension of the array Y. LDY >= N.
*
* Further Details
* ===============
*
* The matrix Q is represented as a product of nb elementary reflectors
*
* Q = H(1) H(2) . . . H(nb).
*
* 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+k1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
* A(i+k+1:n,i), and tau in TAU(i).
*
* The elements of the vectors v together form the (nk+1)bynb matrix
* V which is needed, with T and Y, to apply the transformation to the
* unreduced part of the matrix, using an update of the form:
* A := (I  V*T*V') * (A  Y*V').
*
* The contents of A on exit are illustrated by the following example
* with n = 7, k = 3 and nb = 2:
*
* ( a h a a a )
* ( a h a a a )
* ( a h a a a )
* ( h h a a a )
* ( v1 h a a a )
* ( v1 v2 a a a )
* ( v1 v2 a 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 ..
Method Summary 
static void 
DLAHRD(int n,
int k,
int nb,
double[][] a,
double[] tau,
double[][] t,
double[][] y)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
DLAHRD
public DLAHRD()
DLAHRD
public static void DLAHRD(int n,
int k,
int nb,
double[][] a,
double[] tau,
double[][] t,
double[][] y)