org.netlib.lapack
Class DLABRD
java.lang.Object
org.netlib.lapack.DLABRD
public class DLABRD
 extends java.lang.Object
DLABRD is a simplified interface to the JLAPACK routine dlabrd.
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
* =======
*
* DLABRD reduces the first NB rows and columns of a real general
* m by n matrix A to upper or lower bidiagonal form by an orthogonal
* transformation Q' * A * P, and returns the matrices X and Y which
* are needed to apply the transformation to the unreduced part of A.
*
* If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower
* bidiagonal form.
*
* This is an auxiliary routine called by DGEBRD
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows in the matrix A.
*
* N (input) INTEGER
* The number of columns in the matrix A.
*
* NB (input) INTEGER
* The number of leading rows and columns of A to be reduced.
*
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the m by n general matrix to be reduced.
* On exit, the first NB rows and columns of the matrix are
* overwritten; the rest of the array is unchanged.
* If m >= n, elements on and below the diagonal in the first NB
* columns, with the array TAUQ, represent the orthogonal
* matrix Q as a product of elementary reflectors; and
* elements above the diagonal in the first NB rows, with the
* array TAUP, represent the orthogonal matrix P as a product
* of elementary reflectors.
* If m < n, elements below the diagonal in the first NB
* columns, with the array TAUQ, represent the orthogonal
* matrix Q as a product of elementary reflectors, and
* elements on and above the diagonal in the first NB rows,
* with the array TAUP, represent the orthogonal matrix P as
* a product of elementary reflectors.
* See Further Details.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,M).
*
* D (output) DOUBLE PRECISION array, dimension (NB)
* The diagonal elements of the first NB rows and columns of
* the reduced matrix. D(i) = A(i,i).
*
* E (output) DOUBLE PRECISION array, dimension (NB)
* The offdiagonal elements of the first NB rows and columns of
* the reduced matrix.
*
* TAUQ (output) DOUBLE PRECISION array dimension (NB)
* The scalar factors of the elementary reflectors which
* represent the orthogonal matrix Q. See Further Details.
*
* TAUP (output) DOUBLE PRECISION array, dimension (NB)
* The scalar factors of the elementary reflectors which
* represent the orthogonal matrix P. See Further Details.
*
* X (output) DOUBLE PRECISION array, dimension (LDX,NB)
* The mbynb matrix X required to update the unreduced part
* of A.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= M.
*
* Y (output) DOUBLE PRECISION array, dimension (LDY,NB)
* The nbynb matrix Y required to update the unreduced part
* of A.
*
* LDY (output) INTEGER
* The leading dimension of the array Y. LDY >= N.
*
* Further Details
* ===============
*
* The matrices Q and P are represented as products of elementary
* reflectors:
*
* Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb)
*
* Each H(i) and G(i) has the form:
*
* H(i) = I  tauq * v * v' and G(i) = I  taup * u * u'
*
* where tauq and taup are real scalars, and v and u are real vectors.
*
* If m >= n, v(1:i1) = 0, v(i) = 1, and v(i:m) is stored on exit in
* A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in
* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
*
* If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in
* A(i+2:m,i); u(1:i1) = 0, u(i) = 1, and u(i:n) is stored on exit in
* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
*
* The elements of the vectors v and u together form the mbynb matrix
* V and the nbbyn matrix U' which are needed, with X and Y, to apply
* the transformation to the unreduced part of the matrix, using a block
* update of the form: A := A  V*Y'  X*U'.
*
* The contents of A on exit are illustrated by the following examples
* with nb = 2:
*
* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):
*
* ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 )
* ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 )
* ( v1 v2 a a a ) ( v1 1 a a a a )
* ( v1 v2 a a a ) ( v1 v2 a a a a )
* ( v1 v2 a a a ) ( v1 v2 a a a a )
* ( v1 v2 a a a )
*
* where a denotes an element of the original matrix which is unchanged,
* vi denotes an element of the vector defining H(i), and ui an element
* of the vector defining G(i).
*
* =====================================================================
*
* .. Parameters ..
Method Summary 
static void 
DLABRD(int m,
int n,
int nb,
double[][] a,
double[] d,
double[] e,
double[] tauq,
double[] taup,
double[][] x,
double[][] y)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
DLABRD
public DLABRD()
DLABRD
public static void DLABRD(int m,
int n,
int nb,
double[][] a,
double[] d,
double[] e,
double[] tauq,
double[] taup,
double[][] x,
double[][] y)